model integration and control interaction analysis of ac

Model Integration and Control Interaction

Analysis of AC/VSC HVDC System

A thesis submitted to The University of Manchester for the Degree

of Doctor of Philosophy

in the Faculty of Engineering and Physical Sciences

2015

Li Shen

School of Electrical and Electronic Engineering

- 3 -

Table of Contents

Table of Contents ....................................................................................................- 3 -

List of Figures .........................................................................................................- 8 -

List of Tables.........................................................................................................- 12 -

Nomenclature ........................................................................................................- 13 -

Abbreviations and Acronyms ............................................................................- 13 -

List of Symbols .................................................................................................- 15 -

Abstract .................................................................................................................- 18 -

Declaration ............................................................................................................- 19 -

Copyright Statement .............................................................................................- 20 -

Acknowledgement.................................................................................................- 21 -

Chapter 1. Introduction and Review of AC/DC Interaction ...........................- 23 -

1.1. Transmission with VSC HVDC ............................................................- 23 -

Development of HVDC Technology ............................................................- 23 -

Development of UK Offshore Windfarm Connections and Interconnectors - 25 -

VSC HVDC System Configurations .............................................................- 27 -

HVDC Circuit Breaker ..................................................................................- 29 -

1.2. Review of AC/DC Interaction ...............................................................- 30 -

Modelling of Integrated AC/DC Systems .....................................................- 30 -

VSC HVDC and AC Interactions .................................................................- 31 -

Analysis Techniques .....................................................................................- 35 -

Summary of Past Research on AC/DC Interaction .......................................- 36 -

1.3. Project Background ...............................................................................- 37 -

1.4. Aims and Objectives .............................................................................- 38 -

1.5. Thesis Main Contributions and Publications ........................................- 38 -

- 4 -

1.6. Thesis Outline .......................................................................................- 40 -

Chapter 2. AC/DC Models, Controls and Integration ....................................- 41 -

2.1. Modelling of AC System ......................................................................- 41 -

Synchronous Generators ...............................................................................- 41 -

Generator Control..........................................................................................- 43 -

Branches ........................................................................................................- 44 -

Loads .............................................................................................................- 45 -

Network Modelling .......................................................................................- 47 -

Test System for Generic AC/DC Interaction Study ......................................- 48 -

2.2. Modelling of VSC HVDC .....................................................................- 49 -

Converter Voltage Conversion and Converter Equations .............................- 50 -

Converter Level: Direct control and Vector Current Control .......................- 53 -

Converter Level: Outer Controls and Droop Characteristics ........................- 57 -

2.3. AC/DC System Integration and Model Verification .............................- 64 -

DC Line Model .............................................................................................- 65 -

Integration Method ........................................................................................- 66 -

Integrated Generic AC/DC System ...............................................................- 69 -

Conclusion ....................................................................................................- 71 -

Chapter 3. Dynamic GB System Modelling ...................................................- 72 -

3.1. Background ...........................................................................................- 72 -

3.2. Steady-state System Construction .........................................................- 73 -

Network Branches .........................................................................................- 74 -

Bus Components ...........................................................................................- 75 -

Model Validation ..........................................................................................- 77 -

3.3. Dynamic Generator Design ...................................................................- 77 -

Generator Type Selection ..............................................................................- 78 -

Generator Controls ........................................................................................- 79 -

3.4. Individual PSS Design ..........................................................................- 83 -

Basic Concepts ..............................................................................................- 84 -

Transfer Function Residue Based PSS Design .............................................- 86 -

Example System PSS Tuning .......................................................................- 89 -

- 5 -

Dynamic GB System Characteristics ............................................................- 92 -

GB System with Inter-area Oscillation .........................................................- 94 -

Heavily Stressed System ...............................................................................- 96 -

3.5. Shunt Device Dynamic Modelling ........................................................- 98 -

3.6. Light Loading GB System ..................................................................- 101 -

3.7. Conclusion ..........................................................................................- 104 -

Chapter 4. The Effect of VSC HVDC Control on AC System Electromechanical

Oscillations and DC System Dynamics ..............................................................- 106 -

4.1. Methodology for VSC Control Assessment ........................................- 106 -

4.2. Control Parameterization ....................................................................- 107 -

Modelling of Feedback DC Voltage Loop ..................................................- 109 -

Modelling of Feedback Real and Reactive Loops ......................................- 111 -

Modelling of Feedback AC Voltage Loop ..................................................- 111 -

4.3. Method of Analysis .............................................................................- 112 -

Effects on AC System .................................................................................- 112 -

Effects on DC System .................................................................................- 113 -

4.4. Investigation Based on Generic AC System .......................................- 114 -

Effects of VSC Outer Controls on Inter-area Mode ....................................- 114 -

DC System Effects ......................................................................................- 121 -

4.5. Test Based on Dynamic GB System ...................................................- 124 -

4.6. Effect of MTDC with Different Droop Controls ................................- 128 -

MTDC Grid Control ....................................................................................- 129 -

Power Sharing in DC Grid ..........................................................................- 131 -

Simulation Studies for Wind Power Injection ............................................- 132 -

Simulation Studies for AC System Fault ....................................................- 135 -

4.7. Conclusion ..........................................................................................- 137 -

Chapter 5. Potential Interactions between VSC HVDC and STATCOM ..............

.....................................................................................................- 139 -

5.1. Interactions in HVDC and FACTS .....................................................- 139 -

5.2. STATCOM Model for Stability Studies .............................................- 141 -

5.3. Generic Interaction Study ...................................................................- 142 -

RGA for Plant Model ..................................................................................- 143 -

- 6 -

Outer Control Interactions...........................................................................- 146 -

5.4. Test on Dynamic GB System ..............................................................- 153 -

5.5. Conclusions .........................................................................................- 157 -

Chapter 6. Additional Control Requirements for VSC HVDC - A Specific Case

Study .....................................................................................................- 158 -

6.1. Power Balance between Generation and Demand ..............................- 158 -

Principle of Power Balance in Conventional Power Systems .....................- 159 -

System Power Imbalance with VSC HVDC ...............................................- 160 -

Example Case ..............................................................................................- 162 -

Restoring Power Balance by Generators.....................................................- 164 -

6.2. Restoring Power Balance by VSC HVDC Action ..............................- 166 -

Droop Type Control for AC System Power Support ..................................- 166 -

Proposed Control for Grid Power Support ..................................................- 171 -

6.3. Effects of Ramp Rate Limiter .............................................................- 177 -

6.4. Restoring Power Balance Using VSC HVDC in Dynamic GB System .......

.............................................................................................................- 178 -

6.5. Conclusions .........................................................................................- 184 -

Chapter 7. Conclusions and Future Work .....................................................- 186 -

7.1. Conclusions .........................................................................................- 186 -

AC/DC Modelling .......................................................................................- 187 -

VSC HVDC – AC System Control Interaction ...........................................- 188 -

VSC HVDC - FACTS Control Interaction .................................................- 189 -

7.2. Future Work ........................................................................................- 190 -

Effects of MTDC Systems on AC Networks ..............................................- 190 -

Extended Interaction Studies.......................................................................- 191 -

References ...........................................................................................................- 192 -

Appendix .............................................................................................................- 202 -

Appendix A Power System Stability Basics and Techniques .........................- 202 -

A1. Electromechanical Oscillations ............................................................- 202 -

A2. Modal Analysis Basics .........................................................................- 205 -

A3. QR Method ...........................................................................................- 208 -

- 7 -

A4. Lead-lag Compensator .........................................................................- 210 -

Appendix B VSC Topologies, Losses and Capability ....................................- 212 -

B1. Converter Topology..............................................................................- 212 -

B2. Converter Losses ..................................................................................- 218 -

B3. VSC Capability Curve ..........................................................................- 218 -

Appendix C AC and DC Model Equations .....................................................- 220 -

C1. Sixth Order Generator Equations .........................................................- 220 -

C2. Generator Saturation Characteristics ....................................................- 221 -

C3. Network dq0 Transformation ...............................................................- 222 -

C4. Linearized VSC HVDC Link Equations ..............................................- 224 -

Appendix D Data for Developing Dynamic GB System ...............................- 228 -

D1. Steady-state Data ..................................................................................- 229 -

D2. Dynamic Data .......................................................................................- 237 -

Appendix E List of Publications ....................................................................- 240 -

Word count: 55,743

- 8 -

List of Figures

Fig. 1.1 MMC and SM topology. ..........................................................................- 25 -

Fig. 1.2 NETS Generation mix with different future scenarios [19]. ...................- 25 -

Fig. 1.3 Overview of potential VSC HVDC applications in UK. .........................- 26 -

Fig. 1.4 VSC HVDC link topology. ......................................................................- 27 -

Fig. 1.5 Offshore transmission design strategy. ....................................................- 28 -

Fig. 1.6 Atlantic wind connection modified from [9]. ..........................................- 28 -

Fig. 1.7 Diagram of Nanao Island MMC HVDC project modified from [10]. .....- 29 -

Fig. 1.8 Typical POD controllers for VSC HVDC with (a) local or (b) WAMS based

signals. ...................................................................................................................- 32 -

Fig. 1.9 Frequency control philosophy of Great Britain (GB) system modified from

[37]. .......................................................................................................................- 33 -

Fig. 1.10 Typical PV curve plot. ...........................................................................- 34 -

Fig. 2.1 Synchronous machine stator and rotor circuits. .......................................- 42 -

Fig. 2.2 Generator model and control for stability study. .....................................- 43 -

Fig. 2.3 Unified branch model. .............................................................................- 45 -

Fig. 2.4 System with different dq reference frames. .............................................- 47 -

Fig. 2.5 Kundur’s two-area system model (upper) and thyristor excitation system

with PSS (lower) modified from [20]. ..................................................................- 48 -

Fig. 2.6 Structure of multi-terminal VSC HVDC control system. ........................- 49 -

Fig. 2.7 Converter model for power system stability studies. ...............................- 52 -

Fig. 2.8 Power-angle model. .................................................................................- 53 -

Fig. 2.9 (a) Direct voltage control, (b) Feedback type power angle control. ........- 54 -

Fig. 2.10 Closed-loop block diagram of dq current control. .................................- 55 -

Fig. 2.11 Phase-locked loop. .................................................................................- 55 -

Fig. 2.12 Detailed converter level VSC controls. .................................................- 58 -

Fig. 2.13 Constant DC voltage slack bus control. .................................................- 60 -

Fig. 2.14 Example of voltage margin control. ......................................................- 61 -

Fig. 2.15 Vdc-P characteristic voltage droop control. ............................................- 62 -

Fig. 2.16 Block diagram of droop control. ............................................................- 63 -

Fig. 2.17 VSC AC voltage and frequency droop characteristics. .........................- 63 -

Fig. 2.18 DC line model. .......................................................................................- 65 -

Fig. 2.19 Integrating VSC terminals into AC system. ..........................................- 66 -

Fig. 2.20 Complete diagram of the integrated model............................................- 69 -

- 9 -

Fig. 2.21 Integrated AC/DC test system. ..............................................................- 70 -

Fig. 2.22 Comparison of different integrated AC/DC models (PF Model =

DIgSILENT PowerFactory model). ......................................................................- 70 -

Fig. 3.1 Representative GB network model overview (modified from [72])........- 74 -

Fig. 3.2 Node bus structure. ..................................................................................- 76 -

Fig. 3.3 IEEE type DC1A and ST1A standard excitation systems. ......................- 80 -

Fig. 3.4 Typical turbine governor models. ............................................................- 81 -

Fig. 3.5 Comparison of example system generator speed responses with and without

governors. ..............................................................................................................- 83 -

Fig. 3.6 Linearized Phillips Hefron Model. ..........................................................- 84 -

Fig. 3.7 Standard PSS structure. ...........................................................................- 86 -

Fig. 3.8 Single line diagram for SMIB. .................................................................- 89 -

Fig. 3.9 Root locus for generator 11 PSS gain selection (Positive frequency only). ....

...............................................................................................................................- 91 -

Fig. 3.10 Overview of the developed “dynamic GB system”. ..............................- 93 -

Fig. 3.11 (a) Eigenvalues of original system, (b) Eigenvalues of the system with

inter-area mode (Eigenvalues plot for positive frequencies near 0 only and the

dashed line denotes 5% damping) and (c) Mode shape of inter-area mode. .........- 94 -

Fig. 3.12 Generator speed responses during AC system fault event. ....................- 95 -

Fig. 3.13 System responses when stressed. ...........................................................- 97 -

Fig. 3.14 SVC Model and ideal VI characteristic. ................................................- 98 -

Fig. 3.15 Typical SVC control schemes. ..............................................................- 99 -

Fig. 3.16 Dynamic responses of SMIB system with SVC. .................................- 100 -

Fig. 3.17 Bus 2 voltage and bus 29 frequency responses for a 100ms self-clearing

three-phase short circuit event at bus 24. ............................................................- 103 -

Fig. 3.18 Bus 2 voltage and frequency responses for 1GW ramp up change in 2s in

load 25 .................................................................................................................- 104 -

Fig. 4.1 Full diagram of VSC terminal model and control structure. .................- 108 -

Fig. 4.2 VSC FF type control block diagram representations. ............................- 109 -

Fig. 4.3 VSC FB type control block diagram representations. ...........................- 110 -

Fig. 4.4 Example of closed-loop frequency responses. .......................................- 112 -

Fig. 4.5 Eigenvalue tracking procedure. .............................................................- 113 -

Fig. 4.6 Generic two-area system with embedded VSC HVDC link. .................- 114 -

Fig. 4.7 Tie-line power responses at different operating points. .........................- 116 -

Fig. 4.8 Root loci of inter-area mode with bandwidth variations in individual FB

type control loop at (a) 100MW DC link power and (b) 200MW DC link power. ......

.............................................................................................................................- 117 -

Fig. 4.9 Root loci of the inter-area mode for FBVac cntrol. ................................- 119 -

- 10 -

Fig. 4.10 Root loci of the inter-area mode with FBVac at different locations (DC link

power =100MW). ................................................................................................- 119 -

Fig. 4.11 Effect of FBVac control in different locations (DC link power =100MW). ..

.............................................................................................................................- 120 -

Fig. 4.12 DC side dynamic response comparison of different control schemes for

step change (a-d) and AC system fault (e-h) events. ..........................................- 123 -

Fig. 4.13 Comparison of constant Vdc and droop control. ..................................- 124 -

Fig. 4.14 “Dynamic GB system” with embedded VSC HVDC link. ..................- 124 -

Fig. 4.15 Eigenvalues of the stressed dynamic GB system (eigenvalues with small

negative parts and positive frequencies only) and mode shape plot. ..................- 125 -

Fig. 4.16 Tie-line 8-10 power responses with FF/FB type VSC control. ...........- 127 -

Fig. 4.17 (a) System responses with FBVac control in VSC1 and (b) System

responses with FBVac control in VSC2. ..............................................................- 128 -

Fig. 4.18 Diagram for the integrated GB system and MTDC grid. ....................- 129 -

Fig. 4.19 Vdc-P characteristics for the three control schemes. ............................- 131 -

Fig. 4.20 DC grid power change for different control schemes. .........................- 133 -

Fig. 4.21 Simulation results for 500 MW wind power injection. .......................- 133 -

Fig. 4.22 Simulation results for AC system fault. ...............................................- 136 -

Fig. 5.1 STATCOM model (a) with δ-PM control (b) V-I characteristic. ...........- 141 -

Fig. 5.2 Reduced system model for generic interaction study. ...........................- 143 -

Fig. 5.3 RGA plant model with selected inputs and outputs. ..............................- 145 -

Fig. 5.4 Root loci of system eigenvalues with STATCOM voltage controller gain

varied from 0.1 to 1 with a strong AC network. .................................................- 148 -

Fig. 5.5 Root loci of system eigenvalues with STATCOM voltage controller gain

varied from 0.1 to 1 with a weak AC network. ...................................................- 148 -

Fig. 5.6 Comparison of system dynamic responses with a strong (left) and a weak

(right) AC system. ...............................................................................................- 149 -

Fig. 5.7 System responses with different VSC2 PQ control settings and a weak AC

system. .................................................................................................................- 151 -

Fig. 5.8 STATCOM DC side voltage responses with different VSC2 P control

settings. ...............................................................................................................- 152 -

Fig. 5.9 System responses with different VSC2 P-Vac control settings and a weak

AC system. ..........................................................................................................- 153 -

Fig. 5.10 Dynamic GB system with VSC HVDC link and FACTS. ..................- 154 -

Fig. 5.11 System fault responses for different STATCOM locations. ................- 156 -

Fig. 5.12 System fault responses for different VSC2 controls. ...........................- 156 -

Fig. 6.1 Generator supplying variable load and voltage current phasors diagram. .......

.............................................................................................................................- 160 -

- 11 -

Fig. 6.2 (a) Diagram for specific case study and (b) Representation of power

imbalance in the system. .....................................................................................- 162 -

Fig. 6.3 Test system with VSC HVDC link. .......................................................- 163 -

Fig. 6.4 Test system responses for tie-line disconnection event. ........................- 163 -

Fig. 6.5 VSC HVDC responses for tie-line disconnection event. .......................- 164 -

Fig. 6.6 System responses with steam and hydro type governors. .....................- 165 -

Fig. 6.7 Droop type control to enable VSC HVDC for system power support...- 166 -

Fig. 6.8 System responses with frequency droop control. ..................................- 167 -

Fig. 6.9 System responses with PCC voltage droop control. ..............................- 168 -

Fig. 6.10 VSC control using PMU signal with time delay. ................................- 169 -

Fig. 6.11 System responses with PMU phase angle droop control considering time

delay. ...................................................................................................................- 169 -

Fig. 6.12 Effect of low pass filter for the measured frequency signal. ...............- 170 -

Fig. 6.13 National Grid frequency data. ..............................................................- 171 -

Fig. 6.14 Frequency change in different systems. ...............................................- 172 -

Fig. 6.15 Modified frequency droop control. ......................................................- 172 -

Fig. 6.16 Block diagram representation of the modified frequency droop control. ......

.............................................................................................................................- 173 -

Fig. 6.17 Estimated frequency droop characteristic. ...........................................- 175 -

Fig. 6.18 System responses with modified frequency droop control. .................- 176 -

Fig. 6.19 Rate limiter for d-axis current reference. .............................................- 177 -

Fig. 6.20 Comparison of VSC2 power responses with the effect of rate limiter. .........

.............................................................................................................................- 178 -

Fig. 6.21 Interconnectors in dynamic GB system. ..............................................- 179 -

Fig. 6.22 Designed control schemes for three grid connected converters. .........- 180 -

Fig. 6.23 System responses for a sudden decrease of 40% load demand in a

particular area (VSC HVDC links without designed frequency droop control). .........

.............................................................................................................................- 182 -

Fig. 6.24 System responses for a sudden decrease of 40% load demand in a

particular area (VSC HVDC links with designed frequency droop control). .....- 183 -

Fig. 6.25 System responses for a sudden increase of 30% load demand in a particular

area (VSC HVDC links with designed frequency droop control). .....................- 184 -

- 12 -

List of Tables

Table 2.1 Typical static load models.....................................................................- 46 -

Table 2.2 Estimated control loop bandwidths and limitations. .............................- 50 -

Table 3.1 Main procedures for dynamic GB system modelling. ..........................- 73 -

Table 3.2 Validation between reference case and the developed model (five

significant figures). ...............................................................................................- 77 -

Table 3.3 Example the generator type selection. ..................................................- 78 -

Table 3.4 Resulting generator types. .....................................................................- 79 -

Table 3.5 Eigenvalues for aggregated generator 11 SMIB system. ......................- 90 -

Table 3.6 Full list of eigenvalues for the SMIB system of generator 11 with PSS. .....

...............................................................................................................................- 92 -

Table 3.7 PSS tuning results. ................................................................................- 92 -

Table 3.8 Calculated inter-area mode when system is stressed. ...........................- 97 -

Table 3.9 Summary of generation in different loading conditions. ....................- 102 -

Table 4.1 VSC outer controls and abbreviations. ...............................................- 108 -

Table 4.2 VSC control settings case 1. ...............................................................- 115 -

Table 4.3 Inter-area mode tracking with FF type controls. .................................- 115 -

Table 4.4 Inter-area mode tracking with FB type controls. ................................- 115 -

Table 4.5 VSC control settings case 2. ...............................................................- 116 -

Table 4.6 Inter-area mode damping ratio for case studies in GB system. ..........- 127 -

Table 4.7 Data for MTDC control schemes (Fig. 4.19). .....................................- 131 -

Table 5.1 RGA results for selected inputs and outputs. ......................................- 146 -

Table 5.2 State variables participation factor for the affected modes. ................- 148 -

Table 5.3 State variables participation factor for the affected modes. ................- 149 -

Table 6.1 Proposed frequency droop control settings. ........................................- 176 -

Table 6.2 Interconnector projects in South England. ..........................................- 179 -

Table 6.3 Detailed parameters of the designed control schemes of the grid connected

converters. ...........................................................................................................- 181 -

- 13 -

Nomenclature

Abbreviations and Acronyms

AC alternating current

ACS average cold spell

AGC automatic generation controls

AVR automatic voltage regulator

AWC Atlantic wind connection

CCGT combined cycle gas turbine

CSC current source converter

CSG China Southern Power Grid

CTL cascaded two-level

DC direct current

FACTS flexible alternating current transmission system

FB feedback

FF feedforward

GB Great Britain

GTO gate turn-off thyristor

GOV turbine governing control systems

HVDC high voltage direct current

IEEE institute of electrical and electronics engineers

IGBT insulated gate bipolar transistor

LCC line commutated converters

LPF low pass filter

MIMO multi-input multi-output

- 14 -

MMC multi-level modular converter

MSC mechanically switched capacitors

MTDC multi-terminal DC system

NETS national electricity transmission system

NGET National Grid Electricity Transmissions

ODIS offshore development information statement

OPWM optimal pulse-width modulation

PCC point of common coupling

PLL phase locked loop

PMU phasor measurement unit

POD power oscillation damping

PSS power system stabilizer

PWM pulse-width modulation

RGA relative gain array

ROCOF rate of change of frequency

SCR short circuit ratio

SG synchronous generator

SGCC State Grid Corporation of China

SISO single-input single-output

SMIB single machine infinite bus

STATCOM static synchronous compensator

SVC static VAr compensator

TGR transient gain reduction

- 15 -

List of Symbols

DC System and VSC symbols

Ceq converter DC side equivalent capacitor

Cdc DC cable capacitance

e converter AC side voltage

i converter AC side phase current

kp, kdroop controller proportional gain

ki controller integral gain

P real power

Q reactive power

idc DC current

ia arm current

L inductance

Ldc DC cable inductance

Ls limb inductance

PM modulation index

R resistance

Rdc DC cable resistance

v point of common coupling bus voltage

Vdc DC link voltage

X reactance

θ point of common coupling bus angle

σ angle difference between frames

- 16 -

AC System symbols

A state matrix

B input matrix/susceptance

C output matrix

D feedforward matrix

emf electromotive force

I identity matrix

x state variable/ state vector/ unknowns

u input/ input vector

y output / output vector

λ eigenvalues

Ψ, ψ left eigenvector

Φ, ϕ right eigenvector

ξ damping ratio

Ri residue

Et synchronous generator terminal voltage

Ig synchronous generator terminal current

𝛿 generator/converter AC side angle

Efd excitation voltage

H inertia constant

Pm,e mechanical and electric power

Vpss power system stabilizer output signal

KA,R AC system control gains

f frequency

phi AC bus angle

Vac AC bus voltage

ω speed/modal frequency (imaginary part)

Y admittance

Ta,b,R,w,A,B,TGR time constant

Tm, e mechanical and electrical torque

G(s) plant model

- 17 -

Superscript

* reference quantity of the controller

’ transient

’’ sub-transient

∙ derivative

Subscript

a,b,c electrical phases in three-phase system

dq, DQ direct and quadrature axes (dq domain quantities)

ref reference quantity of the controller

pss power system stabilizer

pcc point of common coupling bus

i,j random numbers

1,2…n various constants

α,β alpha-beta domain quantities

vsc voltage source converter

g synchronous generator

max maximum value

min minimum value

th thévenin equivalent

droop droop gain setting

0 initial value

o operating point value

- 18 -

Abstract

Model Integration and Control Interaction Analysis of AC/VSC HVDC System

Li Shen, Doctor of Philosophy, The University of Manchester, April 2015

The development of voltage source converter (VSC) based high voltage direct

current (HVDC) transmission has progressed rapidly worldwide over the past few

years. The UK transmission system is going through a radical change in the energy

landscape which requires a number of VSC HVDC installations to connect large

Round 3 windfarms and for interconnections to other countries. For bulk power long

distance transmission, VSC HVDC technology offers flexibility and controllability

in power flow, which can benefit and strengthen the conventional AC system.

However, the associated uncertainties and potential problems need to be identified

and addressed. To carry out this research, integrated mathematical dynamic AC/DC

system models are developed in this thesis for small disturbance stability analysis.

The fidelity of this research is further increased by developing a dynamic equivalent

representative Great Britain (GB) like system, which is presented as a step-by-step

procedure with the intention of providing a road map for turning a steady-state load

flow model into a dynamic equivalent.

This thesis aims at filling some of the gaps in research regarding the integration of

VSC HVDC technology into conventional AC systems. The main outcome of this

research is a systematic assessment of the effects of VSC controls on the stability of

the connected AC system. The analysis is carried out for a number of aspects which

mainly orbit around AC/DC system stability issues, as well as the control

interactions between VSC HVDC and AC system components. The identified

problems and interactions can mainly be summarized into three areas: (1) the effect

of VSC HVDC controls on the AC system electromechanical oscillations, (2) the

potential control interactions between VSC HVDC and flexible alternating current

transmission systems (FACTS) and (3) the active power support capability of VSC

HVDC for improving AC system stability.

The effect of VSC controls on the AC system dynamics is assessed with a

parametric sensitivity analysis to highlight the trade-offs between candidate VSC

HVDC outer control schemes. A combination of analysis techniques including

relative gain array (RGA) and modal analysis, is then applied to give an assessment

of the interactions – within the plant model and the outer controllers – between a

static synchronous compensator (STATCOM) and a VSC HVDC link operating in

the same AC system. Finally, a specific case study is used to analyse the capability

of VSC HVDC for providing active power support to the connected AC system

through a proposed frequency droop active power control strategy.

- 19 -

Declaration

No portion of the work referred to in this thesis has been submitted in support of an

application for another degree or qualification of this or any other university or other

institute of learning.

- 20 -

Copyright Statement

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- 21 -

Acknowledgement

First and foremost, I would like to express my sincere gratitude to my supervisors

Prof. Mike Barnes and Prof. Jovica V. Milanović who have been tremendous

mentors for me. Their expertise, invaluable guidance, and patience, added

considerably to my PhD studying experience. My appreciation must also go to Prof.

Keith Bell in the University of Strathclyde for his guidance on network modelling

and insightful comments for this research.

I would like to acknowledge Dr Paul Coventry in National Grid Electrical

Transmission plc (NGET) for sponsoring and supporting this work. He and his team

in NGET have provided me with very useful and valuable suggestions with

industrial context which has greatly strengthened my understanding in this research.

Also thanks go to my fellow researchers (Antony Beddard, Atia Adrees, Bin Chang,

Chengwei Gan, Ding Wu, Jeganathan Vaheeshan, Jesus Carmona Sanchez, Manolis

Belivanis, Oliver Cwikowski, Robin Preece, Siyu Gao, Ting Lei, Tingyan Guo,

Wenyuan Wang etc.) in both Power Conversion (PC) and Electrical Energy and

Power Systems (EEPS) groups at the University of Manchester for their good

companionship, for the discussions and debates we have, and for the exchanges of

knowledge, which all helped enrich my experience of this research work.

Finally but most importantly, I would like to extend my deepest appreciation to my

fiancée Ran Ran and my parents, for their support, encouragement and unwavering

belief in me, which has helped me to get over obstacles and made my PhD far more

enjoyable.

Manchester, March 2015

Li Shen

- 22 -

To my parents

Chapter 1. Introduction and Review of AC/DC Interaction

- 23 -

Equation Chapter 1 Section 1

Chapter 1. Introduction and Review of AC/DC

Interaction

This chapter introduces the background and objectives of the research work. A review

on the state of art and related studies is also provided.

1.1. Transmission with VSC HVDC

Development of HVDC Technology

With the development of high-voltage, high-power, fully controlled semiconductor

devices, high voltage direct current (HVDC) transmission systems have continued to

advance over the past few years. Since the first commercial installation in 1954

(Gotland 1 in Sweden), a vast amount of HVDC transmission systems have been

installed worldwide. The fundamental process that occurs in an HVDC system is the

AC-DC-AC conversion. Two main technologies have been used in the HVDC links

installed so far: (1) line commutated converter based HVDC (LCC HVDC) which uses

thyristor technology [1, 2]; and (2) voltage source converter based HVDC (VSC HVDC)

[3-11], which uses transistors such as the insulated gate bipolar transistor (IGBT).

Because thyristors can only be turned on (not off) by control actions and they rely on

the external AC system to affect the turn-off process, the controllability of LCC HVDC

is limited. The DC current in a LCC HVDC does not change direction. It flows through

a large inductance, and it can be considered almost constant. The converter behaves

approximately as a current source which injects current with harmonics to the connected


- 24 -

AC system. Therefore, it is also sometimes referred to as a current source converter

(CSC). LCC HVDC is normally used in high power rating applications.

The first commercial VSC HVDC project was built by ABB for transmission in 1999 in

Gotland, Sweden [3]. With the self-commutated VSC HVDC technology where both

turn-on and turn-off of the semi-conductors can be controlled, a spectrum of operational

advantages is introduced, notably the ability of feeding passive networks, independent

power control and enhanced power quality. A constant polarity of DC voltage can be

maintained by VSC HVDC. This facilitates the construction of multi-terminal DC

system (MTDC) that is seen as the base for the promising “future DC grid”.

Comprehensive comparisons between practical projects using LCC and VSC

technologies with similar rating are available in [5]. VSC HVDC technology has now

evolved to the point where it is considered the main candidate for the connection of

large renewable energy sources located far-offshore. It is also a leading candidate for

the reinforcement of onshore networks through the use of underground or undersea

cable links. This is likely to result in its widespread proliferation in integrated AC/DC

systems. However, many challenges remain before the potential impact of this change to

system architecture is thoroughly understood.

Since the first appearance of VSC HVDC, there have been several evolutions of

converter topologies introduced by different companies (e.g. Siemens, ABB, Alstom

Grid, etc.). The trend is moving from two-level converter topology towards multi-level

[2]. The advent of multi-level modular converter (MMC) [6, 7] technology enhanced the

quality of the converter output voltage waveform, allowing harmonic filtering

equipment to be reduced or even eliminated. However, in comparison with the two-level

converters, the modelling of MMC becomes more sophisticated [12-15], and more

complicated control systems are required for switching in and out the sub-modules in

the converter arms. Special techniques for additional control requirements such as

capacitor voltage balancing control, circulating current suppression, etc. are proposed

[16-18]. With MMC converters, converter losses are seen reduced to about 1%, which is

comparable to LCC HVDC [7] (see Appendix B2 for further details on converter losses).


- 25 -

The first MMC based commercial project Trans Bay Cable came online in 2010, USA

[8]. The typical MMC converter topology is presented in Fig. 1.1.

SM

SM

SM

SM

SM

SM

SM

SM

SM

SM

SM

SM

SM

SM

SM

SM

SM

SM

idcia

Ls

Sub-Module (SM)

g1S1

S2

DC SM

CapacitorBypass

Switch

DC

Capacitor

Power

Module

CSM

g2

Protection

ThyristorVdc

i

Fig. 1.1 MMC and SM topology.

Development of UK Offshore Windfarm Connections and Interconnectors

The National Electricity Transmission System (NETS) in UK is in a period of radical

change in the energy landscape. Four future scenarios have been created by NETS

considering their affordability and sustainability: Gone Green, Low Carbon Life, Slow

Progression and No Progression [19].

Gone Green Scenario Slow Progression Scenario

Fig. 1.2 NETS Generation mix with different future scenarios [19].


- 26 -

Fig. 1.2 presents the generation mix with the fast developing (Gone Green) and slow

developing (Slow Progression) future scenarios. It is seen that wind generation reaches

approximately 47GW by 2035 (35.5GW of this being offshore) and interconnector

capacity reaches 11.4GW with the Gone Green scenario. Even with a Slow Progression

scenario, the capacity growth in wind and interconnectors by 2035 is still significant —

27GW and 7.4GW for wind and interconnectors respectively.

Firth of

Forth

Dogger

Bank

Hornsea

Norfolk

Rampion

Navitus Bay

Atlantic Array

Celtic Array

Moray Firth

UK Round 3 Wind Farms and HVDC links

Round 3 WF

IFA to France

1986

BritNed to

Netherland 2011

Moyle to Northern

Ireland 2002

Existing links

Future links

EWIC to Ireland

2012

Nemo to

Belgium 2018

ElecLink to

France 2016

IFA2 to France

2019

NSN to Norway

2019

NorthConnect

to Norway 2021

Viking link to

Denmark 2020

FABlink to

Alderney, France

2020

Western Link

Eastern Link

Fig. 1.3 Overview of potential VSC HVDC applications in UK.

The development of UK’s offshore wind power from 2015 is mainly known as the

Round 3 projects (Fig. 1.3), with a potential capacity of 32GW. According to National

Grid’s Offshore Development Information Statement (ODIS) [19], the newly leased

Round 3 offshore windfarm projects normally have large power generation and are

located far from shore, implying potential applications of VSC HVDC transmissions.

NETS also proposes to increase interconnectivity between EU member states to further


- 27 -

secure system operation, facilitate competition and support the efficient integration of

renewable generation. This also gives rise to VSC HVDC technology due to its fast and

independent bidirectional power control capability. The operational interconnectors as

well as the contracted interconnectors are summarized using Fig. 1.3. The two

embedded point-to-point HVDC links – the LCC based Western link and the Eastern

link (planning stage) – are also presented.

VSC HVDC System Configurations

VSC HVDC systems allow independent real and reactive power control. When they are

combined with offshore windfarms or in parallel operation with onshore AC systems,

use of VSC HVDC can benefit the onshore power flows. For instance, power flow in

the AC onshore system may be directed away from areas of electrical constraint by

boosting or restricting power flow in the HVDC systems.

For both onshore-to-windfarm or onshore-to-onshore connections, VSC HVDC systems

are typically configured as a symmetrical monopole, as presented in Fig. 1.4. This type

of topology uses two high-voltage conductors, each operating at half of the DC voltage,

with a single converter at each end. In this arrangement, the converters are earthed via

high impedance and there is no earth current. There are other commonly seen topologies

for HVDC links which are well summarized in [20].

+Vdc

-Vdc

VSC VSCSymmetrical Monopole

Fig. 1.4 VSC HVDC link topology.

The symmetrical monopole configuration has been applied in a number of practical

point-to-point VSC HVDC projects for both onshore and windfarm connections1. The

1 Some typical VSC HVDC projects are:

1) Parallel lines and interconnectors: Trans Bay Cable, Cross Sound Cable, EWIC, Estlink, etc.

2) Offshore windfarm connections: Valhall,Troll A 1-4, Borwin 1, Borwin 2.


- 28 -

symmetrical monopole arrangement is popular with VSC HVDC, but it is uncommon

with LCC HVDC where bipolar topologies are preferred.

Further development of VSC HVDC technology will probably result in MTDC grid.

Different design approaches are proposed in ODIS for windfarm connections, from

stage 1 (point-to-point connections) to stage 3 (interconnected AC/DC cables) are

presented in Fig. 1.5.

Wind Farm Array

HVDC platform

and cable

AC platform and

cable

Onshore Grid Onshore GridOnshore Grid

Stage 1 Stage 2 Stage 3

Fig. 1.5 Offshore transmission design strategy.

The coordinated strategy is essentially a MTDC system which provides alternative paths

for the power from windfarms to the onshore grid when any single offshore HVDC

cable is lost. However, sufficient transmission capacity needs to be ensured to

accommodate the required generation output following an outage. Similar VSC MTDC

configurations are seen in Fig. 1.6 with the Atlantic wind connection (AWC) [9], which

will be built through multiple phases — from a paralleled point-to-point link at the start

to a MTDC grid when completed.

New Jersey

Energy Link

Bay Link

Delmarva Energy Link

Wind Farms

Wind Farms

Wind Farms

Fig. 1.6 Atlantic wind connection modified from [9].


- 29 -

Actual implementation of VSC MTDC is seen in the Nanao three-termal ±160kV

project delivered by CSG (China Southern Power Grid) in 2013, which is based on

MMC converter technology [10, 11]. There are two sending ends and one receiving end

with the corresponding converter rating presented in Fig. 1.7. It can be seen from this

practical case that an “interconnected symmetrical monopole” system topology is

adopted.

Sending end:

Jinniu 100MW

Sending end:

Qingao 50MW

Receiving end:

Sucheng 200MW to

allow expansion

Main Grid

110kV

idc1 idc3

idc2

Vdc1 Vdc3

Vdc2

R3

T3T1

R1

Vac1

AC

AC

Vac2T2

R2

MMC1

MMC2

MMC3

AC

Vac3

Fig. 1.7 Diagram of Nanao Island MMC HVDC project modified from [10].

Another MMC based MTDC project was also constructed in Zhoushan, China, by

SGCC (State Grid Corporation of China) which consists of five terminals with a voltage

rating of ±200kV for integrating windfarm generations located in several surrounding

islands [21].

HVDC Circuit Breaker

For the acceptance and reliability of large scale DC systems, especially MTDC

networks, it is crucial to have HVDC circuit breakers available. Instead of shutting

down the whole DC system1, DC breakers are essential to allow DC grid the ability to

isolate any certain part of the system when a DC fault occurs. When comparing the

requirements for DC breakers to conventional AC system breakers, the main difference

is the absence of a natural current zero. DC breakers need to be able to quickly interrupt

1 Windfarm connections based on VSC HVDC are protected by AC side breakers which de-energise the

whole DC link during fault conditions.


- 30 -

fault current and dissipate the energy stored in the DC system inductors. Different

topologies of DC breaker prototypes are currently under investigation by companies like

ABB [22] and Siemens [23]. However, since there are still no standard DC breakers

commercially available and there are no practical implementations in the HVDC projects so

far, DC breakers are not considered in the DC system models of this research at current

stage.

1.2. Review of AC/DC Interaction

Normal power system operation requires stable and reliable control of both real and

reactive power. To keep its integrity, a balance between generation and demand needs

to be maintained. VSC HVDC technology features its capability of independent real and

reactive control within its capability curve. This can be useful to support the connected

AC system with the best mixture of active and reactive power when required. This

section addresses the state of art and the further work required for modelling and

interaction studies regarding VSC HVDC and AC systems.

Modelling of Integrated AC/DC Systems

The challenge for today’s electric power systems is to seek enhancement in bulk power

transmission capability, renewable generation reliability and flexible power flow

controllability. The option of conventional AC expansion is often limited by

environmental constraints or problems with voltage and power instability. In such cases,

upgrading with advanced VSC HVDC transmission techniques and flexible alternating

current transmission systems (FACTS) become attractive alternatives. This will lead to

integrated AC/DC systems where potential interactions in the system plant models or

controls need to be carefully investigated.

For studies regarding AC/DC interactions, integrated AC/DC system models need to be

developed. This normally begins with building steady-state load flow models and then

develops towards dynamic models. One of the very prominent problems in such process

is the power flow calculation for integrated AC/DC systems. Much work has been done

in this respect for detailed AC/MTDC power flow calculation. A general classification


- 31 -

distinguishes between unified [24-26] and sequential methods [27]. The unified method

includes the effect of the DC links in the Jacobian to solve a combined AC/DC Jacobian

matrix. The equations of an integrated AC/DC system are solved simultaneously in each

iteration process for the unified method, and many techniques have been used to

improve its efficiency. On the other hand, in a sequential power flow method, the AC

and DC equations are solved separately in each iteration. The main advantage is that it

becomes easy to combine new DC power flow algorithms to some well-developed of

AC power flow solution techniques. The AC/DC load flow calculation techniques form

the basis of steady-state AC/DC system models.

Dynamics for conventional AC systems are usually represented by generator dynamics

and many well-developed bench-mark models exist. Depending on the purpose of study

and the time frame of interest, generator controls for voltage or turbine power can be

modelled. On the other hand, generalized dynamic DC system models are also proposed

[28, 29]. These mainly include the converter plant models and their hierarchical control

structures, the DC circuit equations and the AC/DC coupling equations. However,

integrated AC/DC models for power system stability studies in past literature are often

based on either simplified AC systems [27] or simplified DC systems [30], with the

assumption that the bandwidths of the DC system’s components are normally much

higher than the AC system dynamics. It is demonstrated in this study that, even though

the time frame of the controllers in the AC or DC side of the system is different, they

can still have significant impact on each other. To develop a method for integrating

detailed AC and DC system dynamic models is thus necessary and further studies are

required in this direction.

VSC HVDC and AC Interactions

With integrated AC/DC system models, interactions between AC and DC systems can

occur in many ways. Some of these potential interactions will be addressed in this

research.


- 32 -

Power Oscillation Damping (POD)

Both VSC HVDC and FACTS can interact with the connected AC system through

active power control. A potential benefit that results is the capability of providing POD

for the connected AC system [31-36] to improve its electromechanical transient

behaviour (see Appendix A1 for background of power system electromechanical

oscillations). Conventional LCC based HVDC can only provide active power

modulation. This is improved by VSC HVDC where both active and reactive power can

be modulated independently by different POD controllers. Various control algorithms

have been proposed to add POD controllers into the VSC HVDC controller through

supplementary modulation to contribute in damping of the inter-area oscillations in the

power system. More effective damping might be achieved through wide-area

monitoring system (WAMS) based stabilizing control, because remote signals which

contain more effective information of the modes of interest can be utilized as the input

to the POD controller [33-35]. Superior to conventional local POD controllers, multiple

signals can be employed by centralized or decentralized controllers to further improve

damping performance of the overall system. However, the robustness of WAMS-based

damping control needs to be carefully evaluated against potential loss of communication.

In addition, time delay in a wide-area system would be inevitable and may have a

detrimental impact on system stability, and it therefore needs to be carefully considered

in POD control design. Typical types of POD controller for VSC HVDC are presented

in Fig. 1.8.

Rectifier Vdc and Q

control

Inverter P and Q

control

HVDC

system

Power

System

1

2

1

1

n

sT

sT

1

w

w

sT

sTkPOD

Local Signal

(e.g. power flow, line

current or voltage

deviation)

Phase

compensationWashout Gain

Auxiliary Damping

Signals

Limits

Rectifier Vdc and Q

control

Inverter P and Q

control

HVDC

system

Power

System

Auxiliary

Damping

SignalsPOD controller

WAMS Based Multi-input-

single-output controler

Signal

Transportation

Delay

(a) (b)

Fig. 1.8 Typical POD controllers for VSC HVDC with (a) local or (b) WAMS based signals.


- 33 -

However, except for the auxiliary damping controls, the various typical outer controls in the

VSC HVDC can also have effects on the electromechanical behaviour of the connected AC

system. These effects have not been systematically analysed and opportunities therefore

exist for further research to provide recommendations regarding VSC controller designs.

AC Grid Frequency Support

Main grid frequency support is another important subject regarding active power

interaction between VSC HVDC and the AC system. The recent trend of replacing

conventional generation (e.g. fossil coal) by offshore windfarm generation and inter-

connectors will reduce the total inertia of the AC system. This makes the AC grid

vulnerable to a short term power imbalance which arises from sudden changes of loads

and/or generations, leading to more severe frequency fluctuations. Power system

frequency recovery response can be categorized into several stages as shown in Fig. 1.9.

When power mismatch occurs, the first stage inertial frequency response is mainly

provided by the kinetic energy stored in the rotating mass of synchronous generator

(few seconds). Then in the second stage, turbine governing control systems (GOV) and

automatic generation controls (AGC) come into play for recovering system frequency.

This can take up to several minutes. In situations where the system frequency continues

to deviate (e.g. lower than 48.8Hz), low frequency relays will be triggered [37].

Disconnection By Low Frequency Relay

Generation

loss

10s 1min 10minsTime

Fre

qu

ency

(H

z)

50.2

50.0

49.8

49.5

49.2

49.0

48.8Stage 1

Stage 2

Stage 3

Stage 1: Inertial frequency response

Stage 2: Primary & Secondary frequency response

Stage 3: Load frequency controller response

Fig. 1.9 Frequency control philosophy of Great Britain (GB) system modified from [37].

VSC HVDC can contribute to the first and second stages of system frequency control

with its fast power control capability [38]. To enable such function, an initial solution

using synthetic inertia control based on the rate of change of frequency (ROCOF) was

discussed in [39]. For windfarm connections via VSC HVDC, it has been proposed that


- 34 -

the DC link voltage or wind turbine power can in certain circumstances be adjusted

based on main grid frequency variations as proposed in [40] and [41] respectively. An

inertia emulation control strategy was proposed in [42] to make use of the energy stored

in the DC capacitors of the HVDC link, though large DC link capacitance was assumed.

However, these methods have weaknesses in practice and further work with increased

fidelity is required to explore the reliability of the controls in the VSC HVDC for

providing frequency responses.

Power System Voltage Stability

Grid connected VSCs can also interact with the system through reactive power or AC

voltage controls. One important issue with power systems is the voltage stability, which

is defined as the ability to maintain acceptable voltages under normal conditions and

when subjected to contingencies. It is suggested in [43] that by varying the control

strategies employed in the VSC HVDC systems, it is possible to increase the maximum

loadability of an AC system. Grid connected VSCs can be configured as a STATCOM

(AC voltage control mode), which has been studied to be able to enhance the system

static voltage stability margin [44]. Such capability can be demonstrated by plotting the

PV curves of the system under different conditions. An example is shown in Fig. 1.10.

Vo

ltag

e a

t th

e w

eak

est

bu

s

Critical voltage

Load power transfer

Base case

Enhanced PV curve

(via e.g. STATCOM, VSC

HVDC)

Fig. 1.10 Typical PV curve plot.

Control Interactions between VSC and FACTS

With the increasing amount of applications of power electronic based devices in today’s

power system such as FACTS devices, further investigations consider the potential


- 35 -

interactions between VSC HVDC and these devices. At this stage there is still a great

deal of uncertainty regarding the structure of future AC/DC systems. Studies have

shown that there exist potential interactions between conventional LCC based HVDC

and FACTS devices or multiple FACTS devices operating in the same system. The

potential interactions between VSC HVDC systems – with their various control

strategies – and FACTS devices have not been addressed before, and therefore further

work is required in this field.

Analysis Techniques

The components in the AC and DC sides of the system form the non-linear power

system model based on their differential and algebraic equations. To study this,

different power system analysis techniques are used.

Modal analysis is one efficient tool which is most widely used for large system small

signal stability studies. The system is linearized at a pre-defined operating point and

modal analysis allows many tasks to be performed such as determining the modes of

oscillations and the sensitivity of the system to changes in parameters. Modal analysis

also helps to find the root loci for a transfer function and perform model reduction of a

large system. The key point of modal analysis is the location of critical eigenvalues and

eigenvectors of the system which is obtained by solving the following equation:

A - λI Φ = 0 (1.1)

where A is the linearized system state matrix, λ is the eigenvalues and Φ is the right

eigenvector. Different algorithms are proposed to locate the eigenvalues of linearized

system models including the commonly used QR method, the modified Arnoldi method

which utilizes the sparse nature of the power system matrix method, and other

techniques summarized in [20]. Techniques such as mode shape, participation factors

and transfer function residues are used in this research for analysis where needed.

Detailed modal analysis basics are given in Appendix A2.

Frequency domain analysis mainly includes classical frequency domain control theories

such as transfer functions and bode plots. Such control theories are used to determine

the stability of derived single-input single-output (SISO) closed-loop systems. When


- 36 -

dealing with multi-input multi-output (MIMO) systems, which can be decoupled,

methods such as relative gain array (RGA) are used for designing and analysing. These

theories are very well documented in book [45].

Summary of Past Research on AC/DC Interaction

Several gaps in the field have been identified that require further investigation:

i. Studies to date have provided dynamic mathematical models for both AC and DC

systems. However, when integrated AC/DC system models are considered,

simplifications are usually made for either the AC or DC side of the system. For

the potential control interactions to be fully captured, the mathematical integration

of detailed AC/DC dynamic models needs to be developed. Meanwhile, in order

to increase the fidelity and accuracy of this study, a more realistic AC system

model is required.

ii. The effect of VSC HVDC on AC system electromechanical behaviour has been

analysed in many literature works with the focus being put on the supplementary

power oscillation damping controllers. This research identifies that the typical

outer controls of VSC HVDC can also affect the AC system electromechanical

behaviour substantially, and the effect of these control schemes have not been

systematically compared. It is therefore essential to provide an assessment of the

effects of VSC controls on the AC system dynamics.

iii. Potential interactions are identified between conventional LCC HVDC and

FACTS devices. No studies concerning the possible interactions between VSC

HVDC and FACTS are available. Thus further investigation is required in this

field.

iv. A detailed and comprehensive analysis of the capability of VSC HVDC for

providing active power support to the connected AC system is currently lacking.

Appropriate controls schemes which enable VSC HVDC for main grid active

power support need to be designed and implemented in large power systems to

assess their effectiveness.


- 37 -

1.3. Project Background

Offshore windfarm connections in the UK, especially from larger Round 3 windfarm

projects, are setting a number of HVDC transmission challenges. On an immediate level,

the interconnection of windfarms along the coast of Great Britain requires further study.

In the longer term, interconnection to other countries will become much more prevalent

in the UK. These challenges will result in new DC interconnections, both to reinforce

existing links and to make new ones to link to new generation and other networks.

These substantial engineering problems require people who are skilled in both

conventional power systems and the new DC transmission systems.

This PhD research is a 3.5-year project as a part of the National Grid DC Voltage

Research Programme which is fully funded by National Grid, UK. It is closely linked to

two other PhDs’ work in the University of Manchester, as shown in the following table,

to address an integrated AC/DC transmission future.

Projects Subjects

1 Control, Dynamics and Operation of Multi-terminal VSC

HVDC Transmission Systems

2a Control Interactions between VSC HVDC and AC System

(slow electromechanical transients)

2b Control Interactions between VSC HVDC and AC System

(fast electro-magnetic transients)

This work is referred to as project 2a and will focus primarily on electromechanical

transient processes and control aspects of AC/DC networks. This includes investigations

on the integration of AC/DC system models and the effect of DC controls on the

connected AC systems, as well as control strategies to coordinate both the DC terminals

and AC system operation. The modelling work is performed in DIgSILENT

PowerFactory with Matlab for analysis where needed. Internal deliverables are

scheduled for National Grid regarding the progress and outcomes of this research.


- 38 -

1.4. Aims and Objectives

The aims of the thesis are in accordance with the project supported by National Grid

which is mainly focused on addressing the issues raised from the past research of

AC/DC interactions, and targeted at electromechanical transient processes and control

aspects of AC/DC systems. A summary of the objectives are listed as follows:

i. Scoping study and development of operational scenarios – Investigate a range of

probable future scenarios in UK with different levels of penetration of VSC

HVDC and FACTS technology, and identify the key dynamics and fidelity of the

models required.

ii. Development of generic AC/DC models – develop generalized dynamic models

for both AC and VSC HVDC systems. Provide mathematical integration of the

dynamic AC/DC models.

iii. Development of a dynamic GB system model – develop a representative dynamic

Great Britain (GB) system model based on realistic reference load flow data to

increase the fidelity of the study.

iv. Assessment of VSC controls – perform more thorough robustness and sensitivity

studies to compare the effect of VSC controls on integrated AC/DC system

electromechanical dynamics. Provide recommendations for the designs of VSC

controls and their parameterizations.

v. Identification of potential control interactions – analyse potential interactions

between VSC HVDC and FACTS devices considering different system conditions.

vi. Additional control requirements for VSC HVDC in probable scenarios – develop

control strategies for VSC HVDC to enable its capability of providing active

power support for the main grid to improve AC system stability.

1.5. Thesis Main Contributions and Publications

The research carried out in this thesis has contributed to a number of areas regarding the

control and stability of integrated AC/DC systems. The main outcome of this research is


- 39 -

the systematic assessment of the effects of integrating VSC HVDC technology on the

conventional AC system. Some associated work is provided in the form of conference

[C] and journal [J] publications – which are given in Appendix E – and a set of

internal reports for National Grid. The main contributions of this thesis can be briefly

summarized as:

i. A scoping study is performed to investigate a range of probable future AC/DC

scenarios which gives a view of possible future electricity transmission options

for the GB grid [associated work: Internal Report “VSC HVDC Candidate

Scenarios” for National Grid].

ii. An overview of the study AC/DC interactions to date is provided which includes

issues with power oscillation damping, AC grid frequency support, etc.

[associated work: Internal Report “An Overview: Power Oscillation Damping

with VSC HVDC” for National Grid].

iii. A generic method is proposed to integrate VSC terminals into AC systems. A

generic dynamic AC/DC model is developed based on the proposed mathematical

integration method for small signal stability studies [C5].

iv. A dynamic representative GB system model is developed based on the reference

steady stage load flow data [associated work: Internal Report “Design of Reduced

Dynamic Model of GB Network and Integration of VSC HVDC Lines” for

National Grid].

v. The problems to integrate an offshore windfarm via VSC based HVDC systems

into an AC network are identified. The operation principles of the proposed

system are described with the focus being put on the interactions of the control

strategies used in the AC network generators and the DC terminal converters [C1].

vi. The potential control interactions between STATCOM and VSC HVDC operating

in the same AC system are identified and analysed [C2], [C4].

vii. An Investigation of a multi-machine AC system model integrating a four-terminal

VSC HVDC system is performed. The effect of different MTDC control schemes


- 40 -

including voltage margin control and different droop control settings are

compared [C3].

viii. The effect of VSC HVDC outer controls on the AC system electromechanical

oscillations and DC system dynamics is analysed in a systematic way in order to

provide recommendations for VSC outer control selections and parameterizations

[J1].

ix. A frequency based droop setting is proposed and implemented to enable VSC

HVDC links to provide power support for improving AC system stability during

power imbalance situations [associated work: Internal Report “Additional Control

Requirements for VSC HVDC - A Specific Case Study” for National Grid].

1.6. Thesis Outline

There are seven chapters in this thesis. The outline of the remaining chapters is provided

below:

Chapter 2 details the modelling of the key components on both the AC and DC sides of

the system and proposes a mathematical integration method for dynamic AC/DC

models.

Chapter 3 shows the development of a more specific dynamic GB system model with

greater fidelity. The detailed design procedures from a steady-state model to a dynamic

model are presented.

Chapter 4 investigates the effect of VSC outer controls on the integrated AC/DC system

electromechanical behaviours based on the developed models in the previous chapters.

The focus is put on the stability of AC system inter-area oscillation and DC system

transient responses.

Chapter 5 extends the study of interactions from VSC/AC to VSC/FACTS. Potential

control interactions between VSC HVDC and STATCOM are identified and analysed.

Chapter 6 identifies additional control requirements for VSC HVDC in probable

scenarios. A frequency based active power control scheme is proposed and implemented

to improve AC system stability.

Chapter 7 summarizes the thesis and provides suggestions for future work.

Chapter 2. AC/DC Models, Controls and Integration

- 41 -


Chapter 2. AC/DC Models, Controls and

Integration

The power industry today sees an ever increasing number of voltage source

converter based high voltage direct current (VSC HVDC) projects being put into

operation with the conventional AC system. The development of a multi-terminal DC

(MTDC) grid will bring significant influence to the operation of AC power systems.

Therefore, incorporation of VSC HVDC transmission into existing AC transmission

networks has become a main challenge. For power system stability studies,

integrated AC/DC system models with appropriate level of fidelity to capture key

system dynamics are thus required. This chapter details the mathematical models of

the key components for developing typical AC and DC systems, together with their

various control strategies. A method is proposed for combining the mathematical

models to form an integrated AC/DC system targeted at electromechanical transient

studies. To demonstrate the integration method, a test AC/DC system is developed.

2.1. Modelling of AC System

Synchronous Generators

One of the key fundamental components in an AC system model is the generators.

The correct modelling of synchronous generators is a very important issue in the

studies carried out for electrical power systems. The type and accuracy of the

generator models can have great influence on the results of power system

simulations. Lower order generator models are likely to result in a lack of accurate

description of practical operation states. Therefore in order to capture the transient


- 42 -

dynamics in the system, higher order detailed generator models are normally

adopted.

Fig. 2.1 Synchronous machine stator and rotor circuits.

The main circuits involved in a synchronous machine are shown in Fig. 2.1 where θ

represents the angle by which the rotor d-axis leads the phase a stator winding. The

electrical performance of a synchronous generator can be developed based on the

dynamic equations of the coupled circuits in Fig. 2.1 [20]. Usually, a simpler form

of the dynamic equations, to more clearly show the physical picture of the machine,

is obtained through a dq0 transformation. The transformation process can be viewed

as a means of referring the stator quantities to the rotor side, based on angle θ. This

allows inductances to have constant values in the dynamic performance equations,

and the transformed stator quantities to have constant values under balanced steady-

state conditions.

Based on the equivalent circuits of a synchronous machine, the characteristic states

of a generator are defined as the steady-state, the transient state and the sub-transient

state. Machine parameters that influence rapidly decaying components are called the

sub-transient parameters, while those influencing the slowly decaying components

are called the transient parameters and those influencing sustained components are

the synchronous parameters. Generators can be represented by an emf behind a

reactance in each of the three states. To allow the dynamics of the synchronous

r d-axis

q-axis

ikq

ikd

efd

ifd

phase a axis

Rotor Stator

ea

eb

ec

a

b

c

ib

ia

ic

Stator phase b

Stator phase a

field winding

amortisseur

winding

Angular velocity

rotate

Stator phase c


- 43 -

generator to be fully expressed, the conventional sixth order generator model is used

for the studies in this thesis, and it is summarized via the set of equations provided

in Appendix C1.

It should be noted that the mathematical synchronous generator equations do not

consider the effects of stator and rotor iron saturation in order to make the analysis

simple and manageable. However, in cases where generator saturation is of concern,

a representation of the saturation for stability studies is provided for generator

models in DIgSILENT PowerFactory. The parameterization method is detailed in

Appendix C2.

Generator Control

The control systems of generators play a vital role in maintaining power system

stability, and therefore need to be included in the generator models. A general

control structure is presented in Fig. 2.2. The generator connected buses are PV type

buses where the generators interact with the AC system network by injecting power

and controlling the bus voltage. The AC network equations will then be solved to

give the generator currents back.

Exciter

PSS

Et_dq

AC

NetworkSG

Vpss

Ig_dqEfd

Turbine

governor

Pm

Fig. 2.2 Generator model and control for stability study.

The terminal voltage is controlled by means of excitation system through field

current control. This is provided by automatic voltage regulator (AVR) which is

performed through excitation control and acts on the DC voltage that supplies the

excitation winding of a synchronous generator. The variation of the resulting field

current changes the generator emf to control generator output voltage. A voltage

transducer that senses, rectifies and filters the terminal voltage to a DC quantity is


- 44 -

also required for comparing the output voltage to the reference. Meanwhile, a power

system stabilizer (PSS) may be included in the excitation system, with either rotor

speed, accelerating power or frequency as the input signal. PSS provides auxiliary

stabilizing signals to the reference excitation voltage which helps to damp the

generator rotor oscillations in order to improve power system dynamic performance.

Additionally, prime mover governing systems allow generators to modify their

mechanical power input to perform generator speed control. The turbine model may

be included when system frequency is a subject of study. However, for studies that

focus on electromechanical transients (a few to tens of seconds), the turbine power

can be considered as constant during such short periods, allowing the generator

control system model to be simplified.

Branches

AC system branches with voltage difference at the two ends can be modelled as

transformer branches; otherwise, it is a transmission line branch. A simplified

transformer model is used, neglecting magnetizing current and no-load losses. The

model is an ideal transformer with adjustable turns ratio and series impedance that

represents resistive losses and the leakage reactance. The transformer can be

configured as in-phase or phase-shifting depending on the turns ratio configurations.

The AC system’s transmission line model used in this study is the common π circuit

model with lumped parameters [20]. In a balanced system condition, the

transmission lines are normally defined by series impedance and shunt admittance.

The effect of shunt conductance Gij is usually small enough to be neglected in power

system lines. A π circuit line model between bus i and j can be expressed as:

ij ij ijZ R jX (series impedance) (2.1)

ij ij ijY G jB (shunt admittance) (2.2)

However, it is possible to combine the branch models into a unified complex model

[46] which can be used for lines, transformers, and phase-shifters. This unified

model is illustrated in Fig. 2.3.


- 45 -

ij

i iE U e

pj

p pE U e

qj

q qE U e

jj

j jE U e

zij

Yij Yij

Iij Iji

Tji:11:Tij

Bus i Bus j

Fig. 2.3 Unified branch model.

Different parameter settings in the unified model will enable representations for

transmission lines or transformers (e.g. when Tij=Tji=1, the model becomes an

equivalent π circuit for transmission lines). Alternatively, when shunt elements are

neglected and Tij=1, the model becomes a transformer model with the tap changer

located at bus j side and turns ratio Tji : 1. The general current equations of such a

unified model are given as:

2 * 2

2 * 2

( )

( )

ij ij i ij ij j ij ij ij i

ji ji j ji ji i ij ji ji j

I a E T T E y Y a E

I a E T T E y Y a E

(2.3)

where

* * 1

ij ji

ij ji

ij ji

j jp q

ij ij ji ji

i j

j j

ij ji ij

ij

E ET a e T a e

E E

T a e T a e yz

(2.4)

Such level of fidelity of the branches is applicable for general power system stability

analysis carried out in this thesis. A complex transmission line model may be

considered for more detailed studies, when factors like unbalanced system situations

and harmonics are taken into consideration.

Loads

Power system load models are mathematical representations of the relationship

between a bus voltage and the power/current (active and reactive) flowing into the

bus. The load models are generally classified as static or dynamic load models. The


- 46 -

former is preferred for power system transient stability analysis. Static load models

express the active and reactive power at any instant of time as functions of the bus

voltage magnitude and frequency at the same instant. Dynamic load models further

includes past instants, voltage-power relationships and the dynamics of different

load types (e.g. motors, protective relays, etc.).

Static load models can be further categorized into three types as shown in Table 2.1

with the corresponding exponential expressions of the three models. P0 and V0 are

the initial load power and load bus voltage. P and V are the load power and load bus

voltage that vary with time.

Table 2.1 Typical static load models.

Static Load Models Description Exponential load models

Constant

impedance (Z)

Power varies directly with the square of the

voltage magnitude

2

0

0

( )V

P PV

2

0

0

( )V

Q QV

Constant

current (I)

Power varies directly with the voltage

magnitude

1

0

0

( )V

P PV

1

0

0

( )V

Q QV

Constant

power (P)

Power does not vary with changes in

voltage magnitude 0P P

0Q Q

Alternatively, a combination of static load characteristics in Table 2.1 can be readily

expressed in the form of a ZIP model [47]:

2

0 1 2 3

0 0

[ ( ) ( ) ]V V

P P a a aV V

(2.5)

2

0 4 5 6

0 0

[ ( ) ( ) ]V V

Q Q a a aV V

(2.6)

where coefficients a(1-6) can be varied to define the proportion of each type of static

load and thus achieve a combination of different static load models. Frequency

dependent load characteristics can be configured by multiplying the above

expressions by a factor related to the frequency deviation, but this is not considered

for this case.

For general load models in large power systems, in absence of detailed information

on the load composition, the most commonly accepted static load model is to

represent active power with a constant current and reactive power with constant


- 47 -

impedance. The constant current active power represents a mix of resistive and

motor devices (nearly constant MVA). This representation may be shifted towards

constant impedance or constant MVA, if the load is known to be more resistive or

more motor driven respectively.

Network Modelling

A power system network can be converted into an equivalent impedance matrix that

includes the line and transformer branches. This matrix forms the basic network

voltage and current equations. An example equation is shown as:

1 11 12 1 1

2 21 22 2 2

1 2

n

n

n n n nn n

I Y Y Y V

I Y Y Y V

I Y Y Y V

(2.7)

where subscripts are bus numbers, such that Ynn is the self-admittance of bus n and

Yij is the mutual-admittance between buses i and j.

To simplify the three-phase AC network calculation, the network is modelled in the

dq domain based on the dq0 transformation. Models for synchronous machines and

voltage source converters can be added into the network model with their own local

dq reference frame. This requires a conversion between different dq reference

frames, as shown in Fig. 2.4.

AC network global DQ

reference frame

Generators local dq domain

Converters local dq domain

dq frame

conversion

Fig. 2.4 System with different dq reference frames.

Conversion from one dq domain reference frame (D-Q) to another (d-q) takes the

form:

cos sin

sin cos

d D

q Q

v v

v v

(2.8)


- 48 -

where σ is the angle difference between different frames. Detailed explanation of

dq0 transformation and the derivation of the conversion between different dq

reference frames is provided in Appendix C3.

Test System for Generic AC/DC Interaction Study

Based on the mathematical representations derived previously for the key AC

components, a generic test system model can be introduced for power system small

disturbance stability studies, as presented in Fig. 2.5. The model is a small four-

generator, two-area system with detailed system parameters given in [20]. In this

case, generators are modelled as sixth order and employ a typical thyristor excitation

system for voltage control and a PSS for damping. Roughly 400MW power is

transferred from Area 1 to Area 2 through two weak AC tie-lines.

Applying modal analysis for the developed power system results in three

electromechanical oscillatory modes: two oscillatory local modes indicating

generators in each area are oscillating against each other and one inter-area mode of

frequency of about 0.5Hz and a damping ratio less than 5% suggesting that

generators in Area 1 are oscillating against generators in Area 2.

G1

G2 G4

G3

1 5 6

7

8

9

10 11 3

42

L7

C7 C9

L9

25km 10km110km 110km

10km 25km

Two-area AC

System Model

T1 T3

T4T2Area 1 Area 2

400MW

Et

Vref

KAEfd

1

1 RsT

1

1

A

B

sT

sT

kpss

(p.u.)

Terminal voltage

transducer

Transient Gain

Reduction (TGR)

washoutGain Phase

compensation

3

4

1

1

sT

sT

1

2

1

1

sT

sT

1

w

w

sT

sT

Fig. 2.5 Kundur’s two-area system model (upper) and thyristor excitation system with PSS (lower)

modified from [20].


- 49 -

2.2. Modelling of VSC HVDC

VSC HVDC is considered as a suitable solution for connecting large offshore

windfarms that are sited far from the onshore AC grid. The VSC converter topology

design has evolved through many generations and its control strategy is now well

developed. In comparison with conventional line commutated converter (LCC)

HVDC, it has the advantages of a smaller foot print, black start capability,

independent real and reactive power control, and a significantly lower harmonic

level if a modular multi-level converter (MMC) topology is used. In this section, the

mathematical models of VSC HVDC and its control systems are addressed.

Valve (Lower) level control

(Voltage Conversion):

1. Converter switching and modulation.

2. Sub-module control (MMC).

3. Monitor valve and capacitor .

4. Valve protection.

For MMC:

6. Capacitor voltage balancing control.

7. Circulating current control.

Station

ControlSystem Level Control:

1. Coordination of converter station

controls.

2. Set operation and control mode for

converter stations.

3. Start/Close converter stations.

Converter (Upper) Level Control:

1. Droop controls.

2. Outer voltage and power controls.

3. Phase locked loop.

4. Inner current control.

5. Converter protections.

Station Level Control:

1. Control and monitor AC/DC

equipment.

2. Protection of transformers, AC/DC

equipment.

Station

Control

Valve

Control

Converter

Control

Valve

Control

Converter

Control

Higher Level Lower level

Fig. 2.6 Structure of multi-terminal VSC HVDC control system.

The control system for VSCs has a cascaded structure as depicted in Fig. 2.6, with

each higher level of control being no faster than its next inner control level. The

typical controls in each level are also listed in Fig. 2.6. For a wholly decoupled

operation, it is normally appropriate that higher level controls are at least four times

slower than the next inner level [48]. The type of switching control employed for the

innermost voltage conversion process depends largely on the topology of the

converter, with its voltage orders provided by inner current controls in the converter

control level. There are normally several types of typical VSC outer controls being


- 50 -

equipped in a converter station providing different functions (e.g. power and voltage

control). They are switchable depending on the actual applications. The outer

controls reference points may be obtained from local or global higher level control

signals. For instance, a system level “DC grid master control” is a high level control

for coordinating the DC voltages and DC power dispatches. This level of control

often has low bandwidth and is employed to achieve optimised DC grid operation.

Telecommunication systems may be required for future large DC grid in order to

monitor the system’s operating conditions and to schedule new power/voltage orders

for the DC grid. Estimated bandwidths for each level of control are provided in

Table 2.2. As the bandwidths of converter level controls are most relevant to the

power system electromechanical transient behaviours, detailed descriptions and

analysis will be carried out for the controls in this level at later stages.

Table 2.2 Estimated control loop bandwidths and limitations.

Cascaded Structure Bandwidth [48, 49]1 Limitations

Valve switching

control (voltage

conversion)

1kHz to 20kHz

Converter switching frequency

(e.g. ABB HVDC Light OPWM 1050Hz;

Siemens MMC 20kHz in effect)

Converter level inner

current control

10Hz to a few

hundreds of Hz

- Inner voltage conversion process

- Line current measuring speed

- Filtering of line frequency harmonics

Converter level outer

control 1Hz to tens of Hz

-Inner current loop

-Speed of measuring actual quantities

System level control 0.1Hz to less than

1Hz

-Inner power loop

-Coordination software limits

Converter Voltage Conversion and Converter Equations

The Inner voltage conversion process is determined by the converter topology and

its switching control. In fact this is how the AC voltage is synthesized from the DC

1The bandwidths are estimated according to data provided in the reference provided. Some controller

parameters are also available in the provided references for converters at the windfarm side and the

AC grid side.


- 51 -

voltage. This is the innermost basic control loop that is contained in all the other

control loops. In comparison with sine-triangle pulse-width modulation (PWM)

converters, more complex control will be required for MMC converters to ensure

voltage balancing between levels. Taking the sine-triangle PWM converters as an

example, the DC line voltage is usually measured and then fed into the converter to

make a robust and controlled AC output. This can be averaged over one PWM

switching frequency cycle as:

_

1

2ac peak M dcV P V (2.9)

where PM is the modulation index, which is the ratio between the peak value of the

modulating wave and the peak value of the carrier wave.

For power system electromechanical transient studies with VSC HVDC systems,

detailed converter switching processes and the associated dynamics are not key

contributions to the key dynamic behaviour of the overall integrated system. The

computational burden that would be introduced by detailed modelling would

complicate the study of transients – particularly when integrated into large AC

networks – and this would also significantly increase the simulation time.

It has been previously validated in [12] that the averaged-value model can accurately

replicate the dynamic performance of the detailed model for studies of these

transient phenomena. Also, as the number of levels increase in converters like MMC,

the AC side voltage waveforms become more sinusoidal. Therefore, the converter

modelled in this study is a fundamental frequency representation, which is

equivalent to an ideal controlled voltage source (in essence what the MMC is

attempting to reproduce). A capacitor is used to represent a capacitance equivalent to

the detailed MMC model. This is considered as a more than adequate representation

of the MMC type converters for large AC/DC system RMS level stability studies, so

the focus can be put on the outer control loops. The detailed MMC EMT transients

are fast enough to be neglected, and thus the converter topology is not a significant

issue for simulations of integrated AC/DC systems.


- 52 -

iabc

vabc

Ceq

PCC bus

R+jwL

VSC

eabc

idcin

Vdc

Converter Bus

AC system

Pe, QePv, Qv

Fig. 2.7 Converter model for power system stability studies.

From a system point of view, the equations to describe a VSC can be derived based

on Fig. 2.7. The voltage and current relationship across the phase reactor can be

expressed as:

abcabc abc abc

die v L Ri

dt (2.10)

Applying the dq transformation (see Appendix C3):

d d d d

q q q q

e v i iR L L

e v i iL R L

0

0 (2.11)

For a balanced system and a power invariant transformation (i.e. k=√(2/3) in the

Clarke transformation), the relationship between the real and reactive power at the

point of common coupling (PCC) bus and the dq domain voltages and currents can

then be written as:

v d d q q

v q d d q

P v i v i

Q v i v i

(2.12)

Neglecting the losses in the converter, the power injected by the converter into the

AC network is equal to the DC link power, and the DC voltage dynamics are given

by the DC side capacitor. The equations are:

dceq n dc n dc d d q q

dVC i i and i V e i e i

dt

Combining gives:

( )d d q q dc

dc

eq dc eq

e i e i iV

C V C

(2.13)


- 53 -

The equations of phase reactors together with the equations of the DC capacitor give

the key dynamics of a converter. After dq transformation and linearization, the

converter’s dynamic equations are summarized as follows:

2

1 10 0 0 0

1 10 0 0 0

( ) 10 0

dd

d q

q

q d

dc qq d d q q qdc d d

eq dc eq dc eq dc eq dc eqeq dc

d i R edt L L Li e

d i Ri v

dt L L LV v

e e i e i id V e ii

dt C V C V C V C V CC V

dc

(2.14)

where id, iq, Vdc are the key state variables that describe the behaviour of a converter

seen from a system point of view.

Converter Level: Direct Control and Vector Current Control

Several types of control methods have been proposed for VSC HVDC based on the

innermost voltage control loop. Among them, power-angle control (direct control),

which used to be employed in STATCOM applications [50], and dq current control

(vector control) [51] are most investigated.

E V

Z

I

Power Angle Model

EP VP

Fig. 2.8 Power-angle model.

The principle of direct control is to manipulate the magnitude of the converter

output voltage and the phase angle between the VSC and the AC systems. The plant

model for direct control is firstly derived. This is illustrated in Fig. 2.8, which is a

power angle model with complex impedance Z. The power is calculated as:

2 cos cos( )Re( )E E

E EVP S

Z

(2.15)

2 sin sin( )Im( )E E

E EVQ S j

Z

(2.16)


- 54 -

When terminal V is considered as an infinite source (β=0) and impedance Z is

considered as lossless (γ = 90°), the equation is simplified as:

sin

E

EVP

X

(2.17)

2 cos

E

E EVQ j

X

(2.18)

where α is now the phase difference between bus voltages E and V.

The phase angle and output voltage magnitude can be controlled directly or by

feedback type controls as depicted in Fig. 2.9 (a) and (b). The converter AC side

voltage is controlled through the modulation index based on equation (2.9). When a

VSC is connected to a very weak AC network such as a windfarm, it acts as the

source which sets voltage and frequency. This forms a special sub-case of direct

control since the wind turbines in effect control their angles and voltages with

respect to the VSC HVDC system.

/p ik k sVdc

* or P*

Vdc or P

VSC

Switching

Control/p ik k s

Vac*

MP

Plant

Model

Vac

VSC

Switching

Control

MPVac

Vac*

N

D

D

N

1

2dcV

(b)

(a)

Fig. 2.9 (a) Direct voltage control, (b) Feedback type power angle control.

The phase angle is controlled by adjusting the phase shift of the converter AC side

voltage with reference to the output of a phase locked loop (PLL), which is normally

synchronized to PCC bus voltage. This determines the active power flowing into the

VSC, and hence charges and discharges the DC capacitor to maintain a constant DC

voltage. However, due to the cross-coupling between the control parameters, the

power-angle control technique is unable to provide independent control of


- 55 -

active/reactive power. Additionally, due to the lack of a current control loop, direct

control does not provide the capability to limit the current flowing into the converter.

This is part of the reason why another type of control – vector current based control,

which limits the current flowing to some extent – is used in some cases.

Vector control (Fig. 2.10) is a current control based technique, and thus it can limit

the current flowing into the converter. It is also known as “dq current control”. The

control is established by converting the voltages and currents into the dq domain.

For a balanced steady-state operation, the dq voltages and currents are mostly DC

values and thus are easy to control. In case of an unbalanced operation, the positive

and negative components of the AC system have to be considered in the control

system. This requires different controllers for each sequence and a method to

separate them.

XcouplingTc

vabc eabciabc

Vdc

Ceq

abc / dq

PLL

id*

id

PIud ed

*

vd

vdq, idq

iq*

iq

uq

vq

dq current loop

PI

L

Decoupling term

dq / abc

Outer controlsidq

*

eabc*

eq*

Fig. 2.10 Closed-loop block diagram of dq current control.

p ik s k

s

Quadrature

Signal

v sin( ')v

0

1/s '

sin( )x

PLL

cos( )x

sin( ') sin cos ' cos sin 'v v v

Fig. 2.11 Phase-locked loop.


- 56 -

Typically, the balanced three-phase AC voltage is taken at the point between the

converter and the network, as shown in Fig. 2.10. The dq current orders are given by

outer controllers, and the two current loops are decoupled by using the nulling terms

ωLidq to reduce the cross-coupling effect. Ideal nulling might not be necessary as

small residual coupling can be acceptable. The plant model for the current control is

given by equation (2.11); and if PI type current controllers are used, the current

control can be expressed using the following equations:

* *

* *

( )( )

( )( )

d

idpd d d q d

iq

q pq q q d q

ke k i i Li v

s

ke k i i Li v

s

(2.19)

A PLL [51, 52] on the positive sequence fundamental voltage component of the

network voltage is required for the dq transformation to obtain the reference angle.

A typical structure is shown in Fig. 2.11, which reduces the voltage q-axis

component to zero in order to align the reference frame with the d-axis. Normally, a

fast dynamic response and a high bandwidth controller are required. However, there

is always a trade-off between the transient response level and a fast bandwidth.

For current loop controller design, the dq current loop transfer function can be

approximated to a second order equation using the plant model equation (2.11) and

current control equation (2.19). By doing so, the desired damping ratio and natural

frequency of the control loop can be calculated. Typically, this is done by assuming

ki>>skp (in the frequency range of interest), and a standard form is like:

2

* 2 2 2

/

2 ( ) / /

n i

n n p i

k Li

i s s s s k R L k L

(2.20)

However, the current control loop is limited by several factors:

i. The bandwidth, normally adjusted by tuning the current loop controller,

should not be faster than the innermost voltage switching control. A

bandwidth of at least 1/4 of the inner voltage conversion process is normally

appropriate.


- 57 -

ii. The manipulated AC voltage input (edq*) is limited by the range of the DC link

voltage.

iii. Over-current limits are necessary for IGBTs in practice as the software current

limits in the dq domain do not limit the current in real world (abc) quantities

for unbalanced contingencies.

Furthermore, as equation (2.10) is used to derive the dq current control, a pre-

condition of the PLL to obtain an accurate synchronization to the AC system is

assumed. This is not always true during AC system faults or in the case of weak AC

systems. Some difficulties have been experienced by VSC HVDC based on vector-

current control in weak AC system connections. Several advanced control strategies

have been proposed to mitigate such problems with AC grid [53]. Investigations

have shown that the PLL dynamics might have a negative impact on the

performance of VSC HVDC in weak AC system connections. The PLL may also

become inaccurate during fault conditions or unbalanced AC network situations and

the vector control or feedforward outer power loops can be affected in such cases.

Another significant factor which needs consideration in a fuller model is the degree

to which the power converter can be overloaded. Power electronic semiconductors

have low (negligible) thermal mass. Thus there is no ‘free’ short-term overload

capability — any overload capability in current or voltage must be paid for. A

comparison between the vector current control and direct control is given in [54].

Converter Level: Outer Controls and Droop Characteristics

Vector current control provides independent real and reactive power control via the

dq transformation. Based upon this fast inner current loop, different outer power and

voltage control strategies can be applied in various forms depending on the

application (e.g. feedforward type and feedback type outer controls). Droop

characteristics can also be added to provide adjustable reference set points for the

outer control loops for multi-terminal operation. The block diagram representations

are summarized in Fig. 2.12 where the cascaded converter control structure is shown.

In this case, the converter (upper) level control is further divided into 3 parts.


- 58 -

XcouplingTc

vabc eabciabcVdcCeq

abc / dq

PLL

id*

id

PIud ed

*vd

vdq, idq

iq*

iq

uq eq*

vq

PI

L

Decoupling Term

dq / abc

X

PIX*

P*,Q*

ND

ND

vd idq_max

idq_min

Feedback type control

X = Vdc,Vac, P,Q

Feedforward control

Kdroop

Reference set points

dq current loopOuter control loops

Droop & System Level

control

idc

in

AC System

PCC bus sV 0Rs+jXs

System Level

Telecommunications

Droop

Control

Fig. 2.12 Detailed converter level VSC controls.

DC Voltage Feedback Loop

Variations in the DC voltage indicate unbalanced power exchange between the AC

and the DC systems. Thus the power balance in a DC system is kept through

constant DC voltage control [55, 56]. Large variations in the DC link voltage are not

acceptable as this might lead to power imbalance or device failure. Normally, there

is at least one converter in the DC grid that takes the responsibility to maintain a

constant DC voltage. This is achieved by adding an outer controller (PI) to modify

the d-axis reference current input with the measured DC link voltage as a feedback.

Limitations are necessary to avoid unacceptable values of reference current due to

large variations in DC link voltage. As shown in Fig. 2.12, the DC voltage control

can be expressed as:

_* *

_( )( )i dc

d p dc dc dc

ki k V V

s (2.21)

In a point-to-point VSC HVDC scenario linking two onshore networks or a grid

integration of offshore windfarms, the converter connecting to a stronger AC

network is typically configured to regulate the DC voltage. This is because a strong


- 59 -

AC network is more reliable for providing a robust AC side voltage and absorbing

DC grid power.

Real and Reactive Power Controls

Feedforward real and reactive power controls [57, 58] can be modelled using

equation (2.12). They link the converter’s power response directly to the actual

current in the dq domain. Instead of adding an additional PI controller to form a

feedback real and reactive power loop, feedforward type controls contain less

dynamics in theory and have faster responses to converter power variations. Since a

perfect PLL performance is assumed in these controls, they are likely to be affected

when PLL is inaccurate during faults or unbalanced conditions. Care must be taken

though with feedforward control as the notional disturbance vd is not part of an

actual and significant feedback loop.

Feedback real and reactive power controls [59-62] are also used for controlling

converter power to reference values. An additional power loop controller needs to be

designed in these feedback type controls. Extra dynamics and complexity are

introduced by the outer controller, and the bandwidth is reduced in comparison with

the feedforward type power controls.

Feedback AC Voltage Control

AC voltage control [63, 64] is used to regulate the converter AC side voltage. This

requires measuring the AC voltage at the point of connection, and it is preferred in

situations where a grid connected VSC provides voltage support to improve the AC

system stability. With this type of control, the VSCs contribute to mitigate

disturbances in the AC network by supplying reactive power.

Voltage Margin Control

The constant DC voltage feedback control mentioned before is often applied to a

converter to serve as a “DC slack bus” in the DC system. The power injection to the

DC grid varies between the maximum and the minimum capability of the converter


- 60 -

to maintain a constant DC voltage. This characteristic can be illustrated by a Vdc-P

relationship in Fig. 2.13.

Vdc

Vdc_ref

Pmin Pmax

Inverter Rectifier

0

Fig. 2.13 Constant DC voltage slack bus control.

With the development of a DC grid, there will be more converter stations connected

together in the same DC grid forming a MTDC grid. If there is only one converter to

maintain the DC voltage for the whole DC grid, several constraints will appear. The

DC slack converter needs to be sufficiently large in order to compensate the total

power change in the DC grid. A high standard of stability and reliability is also

required for this converter because its loss leads to the collapse of the whole DC grid.

Therefore, as the size of the MTDC system increases, it is not safe to rely on only

one converter to take the full responsibility of DC voltage regulation. The remedy

method for this situation is to use the concept of voltage margin or voltage droop

control.

Voltage margin control is clearly described in [65]. Principally, the voltage margin

approach enables more converters in the DC grid to participate in DC voltage

regulation. In voltage margin control, each converter controls its DC voltage as long

as the power flow is within limits and the DC voltages of the terminals are offset

from one another by a certain voltage margin (some typical examples are available

in [65]). This voltage margin is introduced to avoid interaction between the DC

voltage controllers in different terminals. A typical voltage margin control in a two-

terminal HVDC link is presented in Fig. 2.14. In this case, the power is transferred

from converter 2 to converter 1 and the intersection is the steady-state system


- 61 -

operating point. Converter 1 controls the DC voltage and converter 2 is operating at

its lower limit to control power transfer. It should be noted that line voltage drop

along the DC line is neglected in this example and the voltage margin is exaggerated

for clarity.

Vdc

Vdc_ref1

Pmin1 Pmax10

Vdc_ref2

Voltage Margin

Converter 2

rectifier mode

Converter 1

inverter mode

Operating

point

Pmax2Pmin2

P

Fig. 2.14 Example of voltage margin control.

In a MTDC system using voltage margin control, the role of DC voltage regulation

can be transferred from one converter to another. This occurs when the voltage

regulating converter reaches its power (or current) limit or fails. Examples of this

operation are available in [66] and a recently commissioned MTDC project in China

[10]. However, although the responsibility of DC voltage regulation is transferrable,

voltage margin control is still restricted to allow only one converter to regulate the

DC voltage at any instant. Loss of a DC voltage regulating converter will not

collapse the whole system, but the problem of one converter taking the full

responsibility for the whole DC grid voltage stability remains. Therefore, this type

of control is mainly suitable for small scale DC grid connecting to relatively strong

AC systems. With the development of DC transmission, droop type controls (see

next section) may be more appropriate for large DC grids.

Droop Type Controls

The power or voltage references of the outer control loops can be properly adjusted

according to different power flows or operation scenarios through a cascaded droop

characteristic.


- 62 -

DC voltage droop control [56] has been proposed to resolve the problems

encountered before with voltage margin control. This type of control is especially

useful in multi-terminal DC grid operation as there can be more converters

participating in DC voltage control simultaneously, and thus sharing the duty of

maintaining DC voltage and power balancing. One of the key features of DC voltage

droop control is that the DC voltage of each terminal can be varied within limits. A

typical droop control characteristic is shown in Fig. 2.15.

P

1

ref dc _ ref dc

slope

P P V Vk

Vdc

Vdc_high

Vdc_low

PmaxPmin Inverter Rectifier0

Vdc_ref

Vdc

PPref

Fig. 2.15 Vdc-P characteristic voltage droop control.

A proportional gain (kslope) can be defined for the DC voltage droop control to set the

allowable DC voltage variation for given power limitations. When the power

injection or absorption reaches the limit, the converter turns into power limit mode.

Vdc_ref denotes the no-load reference voltage that should be carefully selected

according to the operational requirements. Actual DC voltage Vdc is measured during

operation and fed back into the droop control to modify the power reference of the

converter. Under this configuration, all converters equipped with DC voltage droop

control response to the power variations in the DC grid. This can be added as a

cascaded outer loop to the power loop as shown in Fig. 2.16. Other structures using

droop characteristics between voltage and current (Idc-Vdc) rather than Vdc-P are also

implemented as seen in [67-70].


- 63 -

Vdc

Vdc_ref

P

P_max

P_min

id_ref

id_max

id_min

1

slope

DroopK

PI

Pmeas

Fig. 2.16 Block diagram of droop control.

However, in a real DC grid, there are always resistances in cables which results in

different DC bus voltages when non-zero power flows through the system. A

specific power flow operating condition is associated with a unique set of DC bus

voltages. This can affect the precise power flow control in steady-state operation. In

order to determine the reference DC voltage set points as well as power set points, a

precise DC grid load flow needs to be carried out for a given load flow condition. A

detailed analysis for this issue is available in [56].

There are also other droop characteristics that can be applied to grid connected

converters to contribute to grid frequency and voltage support. Fig. 2.17 shows the

characteristics of the grid side converter AC voltage and frequency droop control.

PCC bus voltage

Reactive

power Q

injectionabsorption

0

kslope

Vac

QmaxQmin

injectionabsorption

0

kslope

Grid

frequency

PmaxPmin

Active

power P

f

Fig. 2.17 VSC AC voltage and frequency droop characteristics.

AC Voltage Droop Control in a grid connected VSC is analogous to the way a

STATCOM or a static VAr compensator (SVC) adjusts their reactive power output

based on local voltages. The VSC injects reactive power to the grid when the AC

voltage drops, and it absorbs reactive power when the AC voltage rises too high


- 64 -

based on equation (2.22). In this configuration, the VSC helps to enhance the AC

system voltage stability.

_

1( )ref ac ref ac

slope

Q Q V Vk

(2.22)

Frequency Droop Control is also a method of configuring the grid connected VSC to

contribute to grid frequency support together with other AC system power sources

such as synchronous generators and large induction motors. A power dependant

frequency control approach [40] can be adopted. In this control mode, the VSC

needs to coordinate with other frequency control sources in a system, and the

equation is written as:

1

( )ref ref

slope

P P f fk

(2.23)

2.3. AC/DC System Integration and Model Verification

Valuable work regarding the dynamic modelling of either AC or DC systems has

been carried out, and several power flow approaches for steady-state AC/DC

systems have been proposed. However, integrated AC/DC system models for power

system stability studies are often based on either simplified AC systems [28] (e.g.

AC systems are represented by a voltage source behind an impedance) or simplified

DC systems [30] (e.g. DC systems are considered as power injections at the

connected AC buses). Also the integration method has also not been addressed in

detail, even though integrated models are seen in [58, 64]. This is based on the fact

that the bandwidths of the DC system’s components are normally much higher than

the AC system dynamics, allowing one to be simplified for modelling. However,

there might still be possible interactions between the VSC outer control loops with

lower bandwidths and the AC system electromechanical modes. Therefore, an

integration method is introduced in this section to include the cascaded VSC control

structures and AC system controls in an AC/DC stability model where the potential

controller interactions and system dynamics can be captured.


- 65 -

In this section, a generic method is proposed to integrate VSC terminals into AC

systems taking into account the cascaded VSC control structures. The method allows

the VSC models to be developed separately by considering them as voltage-

controlled current injections into the connected AC system, and it therefore provides

an alternative for quickly integrating new VSC models into conventional power

system models. It is valid for integrating an arbitrary number of VSC HVDC

terminals. The developed integrated model is a mathematical model for stability

studies which is linearized at a pre-defined operating point via load flow calculations.

Hence an AC/DC power flow [24-27] needs to be performed first. Modal analysis

techniques can be readily applied to the whole integrated AC/DC model, and the

effects of VSC controls on the AC system power oscillations can be analysed

mathematically.

DC Line Model

Ldc

idc

RdcCdc

VSCi

Vdcj

Cvsc

Cdc

Cdc

Cdc

Cvsc

VSCj

Vdciidc1 idc2

DC line model

Fig. 2.18 DC line model.

In addition to the VSC models introduced before, the DC line model is necessary for

linking VSC terminals to form a DC grid. The DC lines are represented by pi section

models. According to Fig. 2.18, the equation for the DC line circuits are:

1

dci

dc dc dc

VC i i

dt (2.24)

2

dcj

dc dc dc

VC i i

dt (2.25)

dc

dc dci dcj dc dc

iL V V R i

dt (2.26)


- 66 -

where Vdci and Vdcj are both input terms provided by the two connected converters.

The DC line current is calculated and fed back into the converters. Depending on the

number of terminals, the equation can be extended into a matrix which includes all

the line dynamics of the DC grid [28]. In some cases, the capacitance of the cable

Cdc can be combined with the converter capacitance Cvsc for simplicity, and therefore

the dynamics of Cdc are included in the converter DC voltage equation (2.13).

Integration Method

As reviewed in the previous chapter, there exist several AC/DC power flow

algorithms. For integration, a unified AC/DC load flow approach1 is chosen to

calculate the initial conditions of both AC and DC variables in this case. This serves

as an initial operating point for the stability model which will be developed in the

following sections.

The integrated AC/DC model for stability studies is similar to the idea of the unified

AC/DC power flow approach, where the solved DC system equations are combined

into the AC system calculations. However, the dynamics of the DC system need to

be taken into consideration. In this section the integration method is described from

a generic point of view where an arbitrary number of VSC terminals are considered

as current injections to the connected AC system, despite the type of the outer

control loops employed in the VSCs. The AC system solves the network equations

and provides the voltages at the PCC buses back to the DC grid as a reference for

the VSCs and PLLs, as presented in Fig. 2.19.

VSC Model i

AC

network

ivsc

vpcc

VSC Model j

VSC Model k

ivsc

vpcc

ivsc

vpcc

Fig. 2.19 Integrating VSC terminals into AC system.

1 Described in DIgSILENT PowerFactory 15.1 technique reference.


- 67 -

Consider a conventional power system stability model with generators only, the

voltages at the generator buses (PV bus) are initially known from load flow

calculations. It is the generator bus currents and the non-generator bus (PQ bus)

voltages that need to be solved, as presented in equation (2.27). This requires an

iterative procedure to reach the final convergence in load flow calculations. For the

stability model, this can be expressed by linear equations, and it is desirable to

reduce the network by eliminating the nodes in which the current do not enter or

leave.

x

g gK L

T

xL M

I VY Y=

I VY Y

Generator bus

voltages knownTo be solved

Null vector To be solved

(2.27)

In the above equation, the system admittance matrix Y is partitioned into four parts1:

YK, YL, YLT, and YM. Ig and Vx are, respectively, the vectors of system injection

currents (generator currents) and non-generator bus voltages that need to be solved.

Ix is a null vector representing the buses without any current injections. Given the

generator bus voltages (Vg), it is possible to calculate Ig and the rest of the non-

generator bus voltages Vx as:

g K g L xI = Y V +Y V (2.28)

T

x L g M xI = 0 = Y V +Y V (2.29)

Solving the above two equations gives:

-1 T

x M L gV = -Y Y V (2.30)

-1 T

g K L M L g red gI = (Y -Y Y Y )V = Y V (2.31)

where Yred is the reduced admittance matrix that is normally used for conventional

power system stability models. It should also be noted that constant loads in the AC

1 Note that it contains YL and YL

T due to its symmetric nature.


- 68 -

system can be considered as self-admittances of the connected bus, and they can be

added to the original network admittance matrix as:

_ 2

( )i iii load

i

P jQY

V

(2.32)

where subscript ‘i’ stands for bus i.

When VSC terminals are added into the network model (it is assumed that the VSC

terminals are NOT connected at the same buses as the generators), the element Ix is

affected by the current injected or absorbed by each one of them, and it will no

longer be a null vector. If the VSC terminals and generators are nominally connected

at one bus, they can always be split by use of a dummy bus and a small impedance

connection. The network equation is then affected by VSCs. In this case, Ix will still

be a known vector as the current injections from the VSC terminals are known from

the load flow calculations initially. However, it will then be constantly modified

when new current injections from the VSC terminals are calculated. In this way the

system admittance matrix can remain unchanged with VSCs.

When considering the effect of VSC currents, equation (2.29) can be modified as:

and

T

x L g M x

x vsc

I = Y V +Y V

I = i (2.33)

Here [ivsc] is a column vector of n rows (n=number of non-generator buses) that

consists of non-zero elements (i.e. VSC current injections) and zeros. The non-zero

elements will depend on the location of the VSC terminals.

Solving the network equations now gives:

-1 T

x M x L gV = Y (I -Y V ) (2.34)

-1 T

g K g L M x L gI = Y V -Y Y (I -Y V ) (2.35)

This calculates the bus voltages required by VSC terminals as well as the current

required by generators with Ix constantly modified by [ivsc].

The complete integrated system diagram is shown in Fig. 2.20. Generators control

their terminal voltages via AVRs, and provide their bus voltages to the AC network.

The non-generator bus current vector is constantly modified by VSC terminals. This


- 69 -

will then affect the network calculation of the generators’ currents as well as all the

system bus voltages. After solving the network, the voltages at the PCC buses are

then fed back into the VSCs, and the generator currents are fed back to generators.

The above process forms a loop which represents the interaction between the AC

and DC systems during operation.

Et...SG

v1

vn

AC Network

I=YV Ig

Vac for PV bus

vpcc

Synchronous

Generators

DC

network

[ivsc]

VSCs

Vdci

idci

Vdcj

idcj

Fig. 2.20 Complete diagram of the integrated model.

Attention should be given to the directions of the VSC currents which will affect the

signs of the corresponding elements in vector Ix. It is also worth noting that this is a

small signal model, meaning that load flow calculations are required for different

operating points.

Integrated Generic AC/DC System

The integration method was tested by constructing a linearized AC/DC model in

Matlab. The VSC HVDC model is developed based on [12, 64], and it is suitable for

small signal stability analysis. The key state equations as well as some important

parameters used in this point-to-point VSC HVDC link model are provided in

Appendix C4.

Dynamic simulations were used to validate the model against the same model built

in DIgSILENT PowerFactory. The two-area system developed before is used as the

AC system, with a point-to-point VSC HVDC link connected in parallel with the tie-

lines carrying 200MW power from bus 7 to bus 9. Bus 7 and bus 9 are considered as


- 70 -

the PCC buses for the DC link. The integrated system is shown in Fig. 2.21. The

VSCs in the DC link are configured to regulate the DC side voltage (VSC1) and

output powers (VSC2) to the AC system. A complete set of linearized VSC

equations for VSC1 and VSC2 are provided in Appendix C4.

VSC HVDC link

Tc1X1

Tc2X2

VSC_AC2VSC_AC1

CeqCeq

G1

G2 G3

G4

25km 10km110km 110km

10km 25km

T1

T2 T3

T41 5

2 3

46

7

8

9

10 11

L7

C7

L9

C9

Two-area

AC network

AC tie-lines

Area1 Area2

VSC1 VSC2

Fig. 2.21 Integrated AC/DC test system.

A remote AC system self-clearing three-phase short circuit is simulated at bus 1 for

100ms. The DC link voltage will be disturbed due to the variations in the PCC bus

voltage following the AC fault. The DC voltage responses of both integrated AC/DC

models (the mathematical model and PowerFactory model) are presented in Fig.

2.22. Some high frequency components are absent from the mathematical model but

the comparison of the transient response still shows good agreement.

1.8 1.9 2 2.1 2.2 2.3 2.4 2.50.94

0.96

0.98

1

1.02

1.04

1.06

Time(s)

VS

C1

Vd

c i

n p

.u.

Mathematical Model

PF Model

Mathematical Model

PF Model

Fig. 2.22 Comparison of different integrated AC/DC models (PF Model = DIgSILENT PowerFactory

model).


- 71 -

Conclusion

This chapter has presented the basic concepts and mathematical modelling of the

key components in both AC and DC systems. This provides a summary of the

models that were developed in past literature and have appropriate levels of fidelity

for power system stability studies.

The conventional method of AC system modelling is described, including models of

synchronous generator, power system branches, loads and AC networks. A generic

two-area system is firstly constructed as a basis for DC system integration in the

later stage. The second part of the chapter details the analytical VSC HVDC model

for power system stability study. The cascaded VSC control structure has been

explained from the fastest valve level control to the slowest system level control.

Emphasis has been put on the converter level control, which has the bandwidths

most relevant to the power system electromechanical transient behaviours. Various

VSC control strategies have been presented for different applications that will be

analysed further in later chapters.

A novel integration method has been proposed for the developed AC and DC system

models. This method has been demonstrated by constructing a mathematical AC/DC

test system, the dynamic performance of which is validated against a same model

constructed in DIgSILENT PowerFactory. As the state variables in the integrated

model are accessible and power system analysis techniques (e.g. modal analysis) can

be readily applied for analysis, the constructed two-area AC system with a paralleled

VSC HVDC link will serve as a generic test system for further AC/DC control

interaction studies in this thesis.

Chapter 3. Dynamic GB System Modelling

- 72 -



In order to extend the fidelity of the generic AC system modelling, this chapter

introduces the development of a dynamic equivalent representative Great Britain

(GB) like system1 with the intention of reproducing more realistic responses and

power flow constraints. However the simulation should not be so complex as to be

over-burdened with excessive detail in the course of study which actually focuses on

new concepts. Because of the simplifications that are made in this reduced model,

the results should not be regard as accurately representing the behaviour of the real

full system. However, by resembling the full GB network in a reduced model, the

construction of scenarios and the interpretation of results will be easier and more

targeted than using classical benchmark models. In this chapter, detailed

construction procedures of the key network components are described, together with

the associated control schemes. The method of adding “dynamics” to an available

steady-state network is shown. The final dynamic system model exhibits different

characteristics – as the system condition varies – which can be used for the studies

throughout the thesis.

3.1. Background

Instead of using fictitious or historic networks, a reference steady-state network is

modified to become a “dynamic GB system model”. The construction mainly

involves detailed models for generators and shunt devices with their associated

control systems, transmission lines and loads. Power system stabilizers (PSS) in the

1The author would like to gratefully acknowledge Manolis Belivanis and Keith Bell at the Department of Electronic and

Electrical Engineering, University of Strathclyde, for providing the steady state data for the representative model of the electricity transmission network in Great Britain.


- 73 -

synchronous generators are modelled and designed to damp local oscillatory modes

leaving the inherent system characteristic to be reflected clearly. The data of a

reference steady-state model is available in [71, 72] which provides detailed model

data of the 2010 electricity network of GB that anticipates the 2010/11 “average cold

spell” (ACS) winter peak demand loading conditions, as well as the planned transfer

to meet that demand. The steady-state data has been validated against a solved AC

load flow reference case provided by National Grid Electricity Transmissions

(NGET).

To add dynamics into the steady-state network, the main procedures are summarized

in Table 3.1. Details of each step will be discussed in this chapter which is intended

to provide a road map for the method of construction of a dynamic AC system

model.

Table 3.1 Main procedures for dynamic GB system modelling.

No. System Construction Procedures

1 Construction and validation of the reference case steady-state

network model data.

2 Determination of main components modelled at each bus and

their corresponding dynamic parameters.

3 Development and design of dynamic control schemes for

particular components if required.

4

Testing and identification of the system’s main characteristic

features under various conditions. The developed system

should be small disturbance stable initially.

3.2. Steady-state System Construction

The steady-state equivalent system model is firstly constructed to build up the

structure of the system, and it is necessary for the validation against the load flow

data of the reference case. This includes the aspects of generation, loading and losses

in the system. The main structure and the inherent characteristics of the system are

actually determined at this stage. The reference network model is depicted in Fig.

3.1 on top of a GB map, which clearly shows the corresponding locations of the

nodes and transmission lines. Each node is considered as a bus station (PQ, PV and

slack bus) in the steady-state network model, and the nodes are linked by network


- 74 -

branches. For completeness, the full steady-state network data is provided in

Appendix D1.

1 2

3

4

5 6

7

8

10

9

1511

12

13

14

16

18

1719

20

2122

23

29

2827

24

2526

Node Bus:

1 Beauly

2 Peterhead

3 Errochty

4 Denny/Bonnybridge

5 Neilston

6 Strathaven

7 Torness

8 Eccles

9 Harker

10 Stella West

11 Penwortham

12 Deeside

13 Daines

14 Th. Marsh/Stocksbridge

15 Thornton/Drax/Eggborough

16 Keadby

17 Ratcliffe

18 Feckenham

19 Walpole

20 Bramford

21 Pelham

22 Sundon/East Claydon

23 Melksham

24 Bramley

25 London

26 Kemsley

27 Sellindge

28 Lovedean

29 S.W.Penisula

Great Britain

Transmission System

132kV node

275kV node

400kV node

275kV double OHL

400kV double OHL

QB transformer

275kV single OHL

Interconnector

Fig. 3.1 Representative GB network model overview (modified from [72]).

Network Branches

As presented in Fig. 3.1, the model consists of 29 buses, interconnected through 99

transmission lines with 49 double-circuit configuration lines and one single-circuit

line. These transmission lines represent the main routes for the power flows across

the GB transmission system. For a balanced system, the network branches are

defined using parameters for only positive phase sequence resistance, reactance and

shunt susceptance. Winter post-fault thermal ratings that should not be exceeded for

a credible system loading condition are also defined. Most transmission lines in

England (the South part) have a nominal voltage of 400kV, while there are a few

lines in Scotland (the North part) with nominal voltages of 275 kV. Transmission

lines between two buses with different voltage levels are considered to operate at the

voltage level of the higher bus (e.g. a 400kV transmission line is used to connect a


- 75 -

275kV bus and a 400kV bus, and a line transformer is used to step up the 275kV bus

voltage to 400kV). Phase shift (Quadrature Booster) transformers are included at

two branches with two degree phase shift at the locations shown in Fig. 3.1.

Interconnections with external systems through interconnectors are modelled

including the links from the South East of England to France and to Netherlands.

However, the interconnector at bus 5 (from the South West of Scotland to Northern

Ireland) is not included in the reference load flow scenario, and thus it is excluded in

this model. The reference load flow suggests that UK is exporting power to external

systems through the interconnectors, and these interconnectors will be treated as

constant power load.

Bus Components

A typical node bus structure is shown in Fig. 3.2. 24 out of 29 buses have generating

units connected to them. The option of one type of synchronous generator model per

bus is applied, and these buses are configured as PV buses while the rest of the

buses are PQ buses and the slack bus (bus 27). Generator rated power is configured

using the value of “available generation” summarized from the 2010/11 National

Grid Seven Year Statement (SYS). “Effective generation” is calculated by applying

an S factor to the “available generation” (e.g. 0.72 for wind-farms, 1 for normal

generation, 0 for non-contributory generation), and this is the exact generation in the

reference load flow scenario. The generators are all aggregated models which

represent the dominant type of generation in a particular area, and they will be

distinguished by their dynamic parameters. Generator transformers are included in

order to facilitate the utilization of standard generator models with low terminal

voltages in the later stages for dynamic simulations. However, the impedances of

these generator transformers are kept small as they are not the focus of the model

and are less significant in comparison with the transmission line impedances in the

system. Shunt devices – such as mechanically switched capacitors, reactors and

static VAr compensators (SVCs) in the system – have been represented in the model

with what are judged to be appropriate reactive power capabilities at equivalent


- 76 -

locations. At this stage, they are provided to either generate or absorb reactive power

at a given value to match the provided load flow scenario.

Static Var System

TCR

MSR MSC

TSC

Branches/

interconnectors Load

Generating Units

AC System

Node

Bus

Fig. 3.2 Node bus structure.

System demand is modelled directly at the high voltage nodes as constant

impedance static loads with the values given by the ACS winter peak demand

condition. In absence of detailed information on the load composition, static loads

can normally be modelled as constant impedance loads, assuming that the load is

mostly resistive. This representation may be shifted towards constant current or even

constant MVA if the load is most comprised of motor-driven units [47]. Each load

also contains the effects of the reduced parts of the actual network that represent the

series active and reactive power transmission losses on the lines, which are not

shown in this network. More accurate load modelling might be appropriate at a later

stage for in-depth analysis of phenomena considered. Other loading conditions such

as summer minimum demand can be modelled by suitable scaling of the load and

generation power across the entire system. An example of a light loading condition

system model is also presented in this chapter after the winter peak loading

condition system is developed.

At this point, when the network branches and buses are properly configured, the

developed steady-state model is able to, in principle, reproduce the active power

flows and line losses across all the main transmission routes of the GB network.

Furthermore, it preserves active and reactive power transmission losses on the lines

as well as the shunts within the reduced parts of the network. Steady-state load flow

analysis can be performed at this stage. With additional dynamics added into the

system, research on power system control and stability issues can be carried out.


- 77 -

Model Validation

The steady-state equivalent model was constructed in DIgSILENT PowerFactory

(DSPF) and the load flow results were validated against the available reference case

scenario.

Table 3.2 Validation between reference case and the developed model (five significant figures).

Data Total Power Reference Load Flow DSPF Load Flow

Generation Pgen 60294 (MW) 60293 (MW)

Qgen 12363 (MVAr) 12333 (MVAr)

Load Pload 59844 (MW) 59844 (MW)

Qload 40368 (MVAr) 40368 (MVAr)

Loss Ploss 450.50 (MW) 449.13 (MW)

Due to the inclusion of generator and line transformers, the resulting system’s

voltage profile is slightly different from the reference case, causing some elements,

like the switched shunts, to behave differently. This in turn has some effects on the

established reactive power balance. However, as presented in Table 3.2, the

developed model is very close to the reference case scenario in terms of active

power flow and losses. This indicates that both the resulting active power flow in all

transmission lines and the bus angles match the reference case data. The total

installed generation of this network is approximately 75GW with the peak demand

around 60GW. The power is mainly transferred from the North to the South. A

schematic diagram of the GB system power flow is provided in the Appendix D1.

3.3. Dynamic Generator Design

The basic steady-state model offers the basis for the design of a dynamic system

model. To focus on the analysis of electromechanical transients in a balanced system,

the generation units are key components to be further modelled to include transient

dynamics and controls. It should be noted that typical or standard data may be used

during the construction process in absence of actual generation data. Generic control

schemes are also expected to suffice when new concepts or general phenomenon are

explored. Therefore, the results obtained may be considered only as indications of

potential problems.


- 78 -

Generator Type Selection

The generation information is summarized from the 2010 “Seven Year Statement”

(SYS) and a full AC load flow solution provided by National Grid in [73]. The

installed capacity at each bus, provided in the generation information (supplied by

“GB network model” data sheet), is the sum of the power station “transmission entry

capacities” of each generation type in the area of the bus. Such capacity is the

maximum amount of power that a power station is allowed to send onto the UK

network. This information will be used to assess the contribution of various

generation types in the same bus. Following the option of one type of generator

model at each bus, the strategy is to use the generation with dominant output power

to represent the entire generation type at the bus.

The selected generation types are parameterized with the corresponding dynamic

data recommended in [74] to distinguish their dynamic behaviours. The number of

paralleled generators will be determined based on the total available generation. The

final one generator model will have equivalent reactance and inertias of the total

number of paralleled generators. For instance, the generation information of bus 4 is

presented in Table 3.3. The large unit coal of 2284MW is the dominant type of

generation. Therefore it is selected as the generator type for the entire bus. The data

in SYS shows that the large coal generation units in bus 4 are mainly of capacity

around 400-500MW. To meet the total effective generation of the entire bus

(2980MW), seven paralleled large unit coal generators with 400-500MW unit

capacity were considered in bus 4. The specific standard generator type data is

obtained by choosing the best match in [74].

Table 3.3 Example the generator type selection.

Bus Generation Type Available Power

Capacity (MW)

Total

Generation

Selected

Type

4. Denny/

Bonnybridge

Wind Onshore 25.20

2908 (MW)

Large

Unit

Coal×7

Large Unit Coal 2284.00

Pumped Storage 340.00

CHP 259.00


- 79 -

After repeating the selection procedure for all buses with generating units, there are

nine types of resulting dominant generator types in the GB network model which are

summarized in Table 3.4.

Table 3.4 Resulting generator types.

Generation Type Specific Types

Hydro Units H11, H14

Nuclear Units N3

Fossil (Coal) Units F15

CCGT Units CF1, CF2, CF3, CF4

Windfarm Units Converter

It should be noted that bus 6 is dominated by windfarm generation and is modelled

as a static generator. This model represents a group of wind generators which are

connected through a full-size converter to the grid. The reason for such a

representation is that the behaviour of the wind power plants (from the view of the

grid side) is mainly determined by the connection converter. With this representation,

the factors that are important for windfarm designs but do not play a decisive role

for the windfarm responses from a system standpoint are put aside. A typical

independent real and reactive power control [75, 76] is employed for the windfarm

units, which will deliver constant power into the grid.

The final selected equivalent generators in the GB system model consist of five

fossil fuel generators, six nuclear generators, ten CCGTs, two hydro generators, and

one wind generator. All generating units utilize detailed sixth order synchronous

generator models except the wind generator. A detailed summary of the final

generation type selections and the corresponding dynamic data is given in Appendix

D2.

Generator Controls

Satisfactory AC system operation is obtained when system frequency and voltages

are well controlled. Therefore, modelling of generator controls is also essential for

the development of the dynamic system model. This may include the modelling of


- 80 -

excitation system, governors and power system stabilizers depending on the focus of

the study performed.

Excitation System

Generators are equipped with excitation systems for terminal voltage control. The

slower DC1A excitation systems are used in most types of generation in the system

as they have been widely implemented by the industry for coal, gas, and hydro

plants. Large and newly constructed nuclear plants are equipped with fast ST1A

excitation systems, which have a higher gain and smaller time constant. Automatic

voltage regulation (AVR) is performed through excitation control that supplies the

excitation winding of synchronous generators. Standard IEEE parameters

recommended in [77] are used. A detailed block diagram representation of the type

DC1A excitation system is depicted in Fig. 3.3.

1

1R

sT 1

A

A

K

sT

1

EsT

[ ]fd E fd E

E S E K

1

F

F

sK

sT

Et

Vref

VRmax

VRmin

VF

Verror

Efd

1

1r

sT

Et

Vref

1

a

a

K

sT

Vmax

Vmin

Efd

DC1A

ST1A

1

2

1

1

TGR

TGR

sT

sT

TGRExciterTransducer

Delay

Transducer

DelayAVR DC Exciter

Vc

Fig. 3.3 IEEE type DC1A and ST1A standard excitation systems.

The terminal voltage of the synchronous machine is sensed and usually reduced to a

DC quantity. The filtering associated with the voltage transducer may be complex. It

can usually be reduced for modelling purposes to the single time constant TR as

shown in Fig. 3.3. A signal derived from field voltage is normally used to provide

excitation system stabilization VF. An error signal is obtained after subtracting the

stabilizing feedback VF and VC from the reference voltage set point. This error is

amplified by the regulator, with KA and TA as the gain and the major time constant

respectively. The amplified signal is used to control the exciter to provide the


- 81 -

desired excitation field voltage Efd. The exciter saturation function SE[Efd] is defined

as a multiplier of exciter output voltage to represent the increase in exciter excitation

requirements due to saturation.

A type ST1A excitation system is also shown in Fig. 3.3, where the excitation is

supplied through a voltage transducer from the generator terminals with a time

constant Tr. The voltage regulator gain in this case is Ka, which is set quite large

while any inherent excitation system time constant is neglected. This type of

excitation system is simpler but faster than the type DC1A. The parameter data of

the excitation systems can be found in Appendix D2.

Turbine Governors

The inclusion of governor models depends on the subject of research. For

electromechanical transient studies where frequency stability is not considered,

governor models can be omitted since their response time is longer than the

dynamics of interest. It can be assumed that there is sufficient inertia in the AC

system to render changes in frequency small over the time frames modelled.

However, for long term stability studies where frequency is of concern, governors

need to be modelled so that the generation units will respond to system power

mismatches following disturbances.

Since the prime sources of electricity energy supplied by utilities are the kinetic

energy of water and the thermal energy derived from fossil fuels and nuclear fission,

hydraulic turbines and steam turbines are used to represent the governors in the AC

system for different types of generators. Both turbine models are described here.

1

R 1

(1 ) 1

HP RH

CH RH

sF T

sT sT

Speed

Governor

Steam Turbine

ref

Transient Droop

Compensation Gc(s)

Hydraulic

Turbine

1

1 0.5

w

w

sT

s T

1

1 ( / )

R

T P R

T s

R R T s

1

pR

1

1G

sT

Gate

Servomotor

Pm

Speed governor

ref

Valve

Position

Turbine

Torque Tm

Steam Turbine

Governor

Hydraulic Turbine

Governor

Fig. 3.4 Typical turbine governor models.


- 82 -

Fig. 3.4 shows typical hydraulic and steam turbine governor models. The basic

function of a hydraulic governor is to control speed or load by feeding back speed

error to control the gate position. The transient droop compensation enables the

governor to exhibit a high droop (low gain) for fast speed deviations and normal

droop (high gain) in steady-state. Tw here represents the “water starting time”, which

is the time required for a head to accelerate the water in the penstock from standstill

to the operating velocity. The hydraulic turbine is modelled as a classical transfer

function, showing how the output power is related to the changes in the gate opening

for an ideal lossless turbine. Tw normally varies with load, with typical values from

0.5-4s. TG is the main servo time constant typically set to 0.2s. The temporary droop

RT and reset time TR can normally be determined as [20]:

[2.3 ( 1) 0.5] /T w w m

R T T T (3.1)

[0.5 ( 1) 0.5]R w w

T T T (3.2)

where the mechanical starting time Tm = 2H (inertia constant).

A steam turbine converts stored energy of high pressure and high temperature steam

into rotating energy, which is in turn converted into electrical energy by the

generator (Fig. 3.4). The heat source for the boiler supplying the steam can be a

nuclear reactor or a furnace by fossil (e.g. coal, oil, gas). Hence the steam turbine

model can be used for generation of type CCGT, fossil, nuclear etc. The control

action is stable with normal speed regulation of 5% droop, and thus there is no need

for transient droop compensation. FHP is the fraction of the total turbine power

generated by high pressure sections, which is normally of value 1/3. TRH is the time

constant of reheater, which is also the most significant time constant encountered in

controlling the steam flow and turbine power. In comparison, TCH (time constant of

main inlet volumes and steam chest) is normally small and can be neglected. Fig. 3.5

exemplifies the speed responses of a synchronous generator supplying an isolated

load with different turbine governing models. A 140ms three-phase fault was

applied at the high voltage end of the connection transformer.


- 83 -

900MW SG

0 2 4 6 8 10 12 14 16 18 200.995

1

1.005

1.01

1.015

1.02

1.025

Time(s)

Ge

n s

pe

ed

p.u

. No Gov

With Hydraulic Gov

With Steam Gov

Tc

SG

Efd

Vload_busEt

Load

Steam Turbine

Governor

Hydraulic Turbine

Governor

Pm or Tm

Fig. 3.5 Comparison of example system generator speed responses with and without governors.

Power System Stabilizer

Power system stabilizers add damping to the generator rotor oscillation by

controlling the excitation voltage through auxiliary stabilizing signals. The actual

GB system is in fact a very stable system with properly tuned local modes.

Therefore, for generators with unstable or poorly damped local modes, PSSs are also

required to be designed. Some techniques are used for determining the parameters of

the PSSs. This is specified in the following section. The inherent characteristics of

the system are then examined after the local modes are properly damped.

3.4. Individual PSS Design

The design of each PSS is based on a mathematical single machine infinite bus

(SMIB) model established for every generator in the GB system. The operating

point of each SMIB is made the same as the corresponding generator in the GB

system, and their parameters are scaled accordingly to the number of generators in

parallel at each bus. A residue based designing technique is addressed in this section,

and the resulting designed PSSs are put back into the GB system model. Turbine

governor models are not included at this stage for PSS tuning, and thus the

mechanical turbine power inputs for the generators are configured to be of constant

values.


- 84 -

Basic Concepts

Tuning of the PSS has been a well-developed research area, and various methods

have been proposed ranging from classic linear control [78, 79] (e.g. residue,

frequency responses based method) to more complex theories [45] (e.g. Linear

Matrix Inequalities, Model Linear Quadratic Gaussian method). However, in

practice, classical tuning methods are overwhelmingly used by engineers due to their

simplicity and applicability. As the basics of all other tuning methodologies, the

classical control analysis theories are preferred at early stages of system design.

They are therefore used here since the target of adding PSSs in this study is to reflect

the essence of the system, but not to optimize the system behaviour.

The basic concept of damping torque provided by PSS in synchronous generators is

described by the Phillips Hefron Model [80, 81], as presented in Fig. 3.6, which

relates the concepts of small perturbation stability of a single machine supplying an

infinite bus through external impedance with the effects of excitation voltage. The

concept of synchronizing and damping torques can be introduced based on this

model [81].

1

MS

377

S

Speed( . .)

mT p u

1K

Rotor angle

2K

5K

6K

4K

3

'

31

do

K

SK T

'

qE

fdE

tE

D

Phillips Hefron Model

Fig. 3.6 Linearized Phillips Hefron Model.

At any given oscillation frequency, braking torques are developed in phase with the

machine rotor angle and rotor speed. Torques in phase with the machine rotor angle

are termed as synchronizing torques, whereas damping torques are developed to be


- 85 -

in phase with rotor speed. Any torque oscillations can be broken down into these

two components, and a resultant stable system indicates a balance between

synchronizing and damping torques.

Fast responding exciters equipped with high gain normally increase the synchronous

torque coefficient of the system, resulting in reduced levels of stability. The purpose

of a PSS is to introduce a damping torque component to counteract this effect

utilizing the generator’s speed signal. This is achieved by adding an auxiliary signal

to the exciter’s input voltage. Appropriate phase compensation is required in PSSs to

compensate for the phase lag between the exciter’s input and the electrical torque. A

block diagram in Fig. 3.7 shows the typical structure of PSS that consists of four key

components: a phase compensation block, a signal washout block, a low pass filter

block and a gain block.

The stabilizer gain Kpss determines the amount of damping introduced by the PSS.

Normally, the damping effect increases with the stabilizer gain — up to a certain

point beyond which further increase in gain will lead to a decrease in damping.

Ideally, the stabilizer gain is set at a value corresponding to maximum damping.

However, the gain is often limited by other physical considerations. The washout

block in the PSS acts as a high pass filter to only allow signals associated with

oscillations in the input signal to pass unchanged. This way, the steady-state changes

in the input signal do not affect the terminal voltage through PSSs. A suitable setting

for the time constant Tw would be a proper value that is long enough to achieve its

filter function, but not so long that it leads to undesirable generator voltage

excursions during system-islanding conditions [20]. Sampled frequency responses of

typical washout blocks are also shown in Fig. 3.7, where the bandwidth is seen

increased with higher Tw value. For initial settings, Tw = 1.5s is enough for local

mode oscillations in the range of 0.8 to 2 Hz, while Tw = 10s or higher should be

used for low frequency inter-area oscillations. A PSS may also include a low pass

filter which is used to prevent interaction with high frequency (usually torsional)

modes. This together with washout block minimise the interaction of the control

signal with the rest of the system beyond 0.2-2.5Hz.


- 86 -

Kpss

1

1

A

B

sT

sT

1

1

sT

saT

Gain

PSS input

Washout Low Pass

Filter

Lead Lag

Compensator

NPSSmax

PSSmin

Vpss1

w

w

sT

sT

Power System Stabilizer

10-3

10-2

10-1

100

101

-50

-40

-30

-20

-10

0

(d

B)

(Hz)Frequency(Hz)

Mag

nit

ude(

dB

)

1.5s

1 1.5s

10s

1 10s

0.0159Hz 0.106Hz

Typical Washout Block Frequency responses

Fig. 3.7 Standard PSS structure.

As previously mentioned, to damp rotor oscillations, the PSS must produce a

component of electrical torque in phase with the rotor speed deviation. Therefore,

there are phase compensation blocks included to provide an appropriate phase-lead

characteristic to compensate for the phase lag difference between the exciter input

and the resulting electrical torque. The phase lag is normally caused by frequency

dependent gain and phase characteristics exhibited in both generators and exciters.

For a small degree of phase compensation, a single first order compensator may be

enough. This number can increase when larger phase compensation is required. The

compensated phase value normally varies to some extent with different system

conditions. Slight under-compensation is usually preferred so that the PSS does not

contribute to negative synchronizing torque component [20].

Transfer Function Residue Based PSS Design

Among the many classical techniques for PSS design, the transfer function residue

based implementation method is to be used for the GB system damping controllers

[79, 82]. The concept of residue is described in Appendix A2 and briefly reviewed

here. A single open-loop transfer function can be extracted from a multi-input multi-

output system as shown in equation (3.3), where the residue at the pole λi is defined


- 87 -

as Ri. According to control theory, the residue provides information regarding the

angle of departure as well as the magnitude of the shift of the eigenvalues. Therefore,

the idea here for damping controller PSS design is to achieve desired shifting of the

critical poorly damped or unstable modes based on their corresponding residue value:

1

1

( ) ( )n

i

i i

RG s C sI A B

s

(3.3)

The residue can also be calculated by the eigenvectors if the state variables are

expressed using the transformed state variables where each one state is only

associated with one mode. This is given as:

i i iR C B

(3.4)

The PSS feedback signal is required to enable a large impact on the residue of the

target mode in order to obtain sufficient controllability over the mode of oscillation

to be damped [83]. As previously discussed, the transfer function of PSS takes the

following form:

1

( ) ( ) ( ) ( )( )1 1

N Nw

pss

w

sT TsH s K W s L s K

sT Ts

(3.5)

The time constant of the washout block is pre-set and the low pass filter is not

included in this case as torsional interactions are not considered. Kpss is the gain of

PSS, which will be determined by the amount of damping required during the tuning

process. An appropriate number of phase lead-lag blocks L(s)N will be designed to

provide adequate phase compensation. Therefore, the parameters that need to be

determined during the tuning procedure are: Kpss, T, and α. The PSS is designed for

the exciter control loop compensation. The implementation is based on transfer

function residues, Following Lyapunov’s first method for system stability. Unstable

or poorly damped modes are shifted to be more damped in the left half-plane. The

amount of shifting can be expressed by the residue of the open loop transfer function

according to the following equation [79].

( )i i iR H (3.6)


- 88 -

where ∆λi is the corresponding eigenvalue shift with H(λi) as the transfer function of

PSS. Ri is the residue of the open loop transfer function corresponding to λi.

The residue of the transfer function between the exciter input voltage ∆Vref and

output speed ∆ω can be calculated via equation (3.4), based on which the

corresponding residue phase angle of critical eigenvalues is identified. These modes

should be shifted towards the left without any changes in frequency for best

damping effect [82], indicating that the shift direction needs to be ±180°, and that it

requires proper phase compensation in PSSs. A phase lead-lag block which takes the

form of L(s) in equation (3.5) is used. Depending on the value of α, L(s) can be

either a phase lead block (T>αT) or a phase lag block (T<αT). The maximum phase

lead or phase lag occurs halfway between the pole and zero frequencies of L(s), and

this should be targeted at the frequency of the critical eigenvalues. A discussion of

the frequency characteristics of a typical phase lead-lag compensator and the effects

of its parameter settings in the frequency domain are provided in Appendix A4.

To ensure a shift direction of ±180°, the required compensation phase angle θpss is

determined after calculating the residue angle. The value of α in the lead-lag

compensator needs to be properly set, so that the maximum phase compensation

occurs at the particular frequency ωi of targeted critical modes (λi=σi±ωi) [82]. This

method is briefly summarized as follows:

180pss residue (3.7)

1, 60

2, 60 12057

3, 120 180

pss

pss

pss

pss

N

(3.8)

1 sin1

1 sin

pss

pss i

N T

N

(3.9)

The compensation angle per lead-lag block should normally be restricted within 0°-

57° to ensure an acceptable phase margin and acceptable noise sensitivity at high

frequencies. This is limited by the value of α (0.087< α <10 to avoid excessive


- 89 -

noise interference). Once the phase compensation is determined, the gain of PSS Kpss

can be found by plotting the root locus of the system voltage-speed loop with the

designed PSS as a feedback. The damping normally increases with the stabilizer

gain. However, the gain of PSS is also restricted in order to limit the interactions

with other controllers. The final value of the gain is set to effectively damp the

critical system modes without compromising the stability of other system modes or

causing excessive amplification of signal noise (typically Kpss is set less than 50).

Example System PSS Tuning

An example of PSS tuning for one of the generators in the GB system is provided

here to demonstrate the key procedures discussed before. In this tuning process, the

criteria of 5% minimum damping ratio is applied for all system modes as

electromechanical oscillations with damping ratios greater than 5% are considered

satisfactory in a power system [84]. With such a damping ratio, the oscillation in the

system will decay in about 13s. For the case of PSS tuning for the generators in the

GB system, the SMIB equivalents are investigated. Generators with poorly damped

(damping ratio <5%) or unstable modes are further designed with a PSS for

improved stability.

Connection

Transformer

Infinite

Bus

Aggregated Gen11

Exciter

PSS

Et

SGVref

Vpss

Efd

Constant Pm

Fig. 3.8 Single line diagram for SMIB.

Aggregated generator 11 is used as an example here (Fig. 3.8). This is a nuclear type

generator which is equipped with type ST1A excitation system. An equivalent SMIB

mathematical model was developed to represent the paralleled machines at bus 11.

The aggregated generator model has inertia (H) and impedance scaled from the


- 90 -

original standard machine, based on the number of paralleled generators. Time

constants of the standard machine remain unchanged. The resulting aggregated

generator model has output real power equivalent to the effective generation given

by the total number of paralleled generators in bus 11 (4576MW) in the load flow

scenario. Furthermore, the branch impedance needs to be properly adjusted so that

the voltage and reactive power flow conditions of the equivalent model are the same

as the case in the GB system model. Eigenvalue analysis of the equivalent SMIB

model results in a pair of unstable eigenvalues, as shown shaded in Table 3.5. The

pair of unstable eigenvalues represents the critical electromechanical modes of this

system that will cause the system to go unstable. These modes need to be damped by

a properly designed PSS that compensates the excitation loop of the system with the

form of:

1

( )( )1 1

Nw

pss

w

sT TsK

sT Ts

(3.10)

Table 3.5 Eigenvalues for aggregated generator 11 SMIB system.

No. Eigenvalues Damping Ratio %

λ1 -2883.4 100

λ2 -2861.1 100

λ3 -33.947 100

λ4 -5.0771+12.417i 37.85

λ5 -5.0771-12.417i 37.85

λ6 -12.95 100

λ7 0.37695+6.385i -5.89

λ8 0.37695-6.385i -5.89

λ9 -0.80765 100

The value Tw for the washout block is pre-set to a typical value of 10s. Calculating

the residue of the transfer function with input Vref and output ∆ω results in Ri = -

0.14+j0.06 where the residue angle is 157.24°. Therefore, the phase compensation

required in this case is 180°-157.24° = 22.76°. To provide this phase compensation

for the targeted eigenvalue at frequency ωi=6.385 (rad/s), a PSS phase lead block

can be determined using criteria equations (3.8) and (3.9). The results are calculated

as:

N=1, 𝛼=0.442, T=0.236.


- 91 -

To determine the gain Kpss, the root loci of the transfer function between the

generator reference voltage and output speed with PSS as feedback is plotted (Fig.

3.9). The gain is increased until the critical modes reach the desired location in the

stable area. Meanwhile, some other stable modes may go unstable or become less

damped as the gain of PSS increases. The method adopted here is that the gain of

PSS is set to a value of 30% to 35% of the critical gain (when the other modes reach

the stability boundary). In this case, as the gain increases, the unstable eigenvalues

0.377± j6.386 shift to the left half-plane with damping ratio greater than 5% (dashed

line). However, another pair of eigenvalues -5.077± j12.42 is shifting right to be

poorly damped with a critical PSS gain value of Kpss=28. Therefore, the PSS gain is

set to a value of Kpss=28×30%=8.4 to avoid other system modes going unstable.

-8 -7 -6 -5 -4 -3 -2 -1 0 1

0

5

10

15

20

0.05

Root Locus

Real Axis

Imagin

ary

Axis -5.077+j12.42

K=0

Damping Factor

K=28K=30

K=0

K=30

0.377+j6.385

Fig. 3.9 Root locus for generator 11 PSS gain selection (Positive frequency only).

Adding the designed PSS, the full list of the SMIB system eigenvalues is shown in

Table 3.6, where the initial unstable modes are properly damped without excessively

deteriorate other system modes. This process needs to be carried out for the rest of

the generators in the GB network model. The equivalent SMIB mathematical model

(Fig. 3.8) will be repeatedly used but with different parameters settings for other

aggregated generator models. For those generators with no poorly damped or

unstable modes, PSSs are not required. The results of all necessary PSS parameters


- 92 -

are summarized in Table 3.7, and these PSSs are put back into the full GB system

model so that all the local modes in the system can be well damped.

Table 3.6 Full list of eigenvalues for the SMIB system of generator 11 with PSS.

No. Eigenvalues Damping Ratio %

λ1 -2883.4 100

λ2 -2861.1 100

λ3 -34.649 100

λ4 -2.1123+13.755i 15.18

λ5 -2.1123-13.755i 15.18

λ6 -12.516 100

λ7 -11.561 100

λ8 -1.4755+5.4509i 26.13

λ9 -1.4755-5.4509i 26.13

λ10 -0.80553 100

λ11 -0.10064 100

Table 3.7 PSS tuning results.

Gens Kpss Tw T 𝛼T Number

of L(s)

G2 16.52 10 0.044 0.240 2

G3 3.68 10 0.633 0.064 3

G11 9.33 10 0.236 0.104 1

G12 22.31 10 0.033 0.210 2

G16 4.68 10 0.657 0.122 3

G19 3.83 10 0.965 0.146 2

G20 6.97 10 0.258 0.085 1

G22 3.57 10 0.491 0.065 3

G23 19.87 10 0.034 0.453 3

G26 15.76 10 0.034 0.191 2

G27 10.93 10 0.259 0.212 1

G28 21.34 10 0.037 0.289 2

Dynamic GB System Characteristics

The dynamics of the reduced GB network model are established with the detailed

generator models and the controls. As it is difficult to get access to the data that is

owned by generating companies, and excessive to model a full real time network,


- 93 -

standard generator and control data are considered to be detailed enough for general

dynamic and stability studies. The developed model enables initial stage modelling

of many key phenomena of new technologies, such as renewable generation and

VSC HVDC integration that are associated with the GB-like AC system. An

overview of the developed dynamic system model is given in Fig. 3.10.

The whole system at this stage has 230 total states which include the dynamic

models of all generating units with their corresponding control systems. Among

these eigenvalues, 23 of them would be electromechanical modes as there are 24

generators in the system (one generator, G27, is configured as the slack generator for

reference). It should also be noted that generator 6 is modelled as a windfarm

connected through a converter, which means this generator will not be visible,

leaving only 22 electromechanical modes.

27

26

2829 C

NN C

1 2

C

H

3

F

4

5

N 6

WF

7

8N

9 10

C11

N

15

F

12

13 14

C

16

C

1917

C

2022

21N

C

C

F

18

F

23

24

25

F C

H

OHL

Bus

Transformer

Load & Shunt

Phase Reactor

H: Hydro

F: Fossil Coal

N: Nuclear

C: CCGT

WF: Wind Farm

Fig. 3.10 Overview of the developed “dynamic GB system”.

The established GB system is well damped by the designed PSSs which is true for

the actual real system. However, there might be inherent stability problems if the

system condition varies. Therefore, when analysing the stability issues, different


- 94 -

possible system scenarios are considered which will push the system to its stability

margins, and the inherent characteristics of the system may become more obvious in

those cases. These conditions are detailed below.

GB System with Inter-area Oscillation

The first “weakened” system condition is one with reduced number of PSSs, in

which case the system’s damping torque is reduced. A low frequency inter-area

mode is detected in the system in a particular case where the PSS in the generator at

bus 16 (shaded in Table 3.7) is removed. This PSS has the largest participation

factor to the low frequency mode of the originally developed system, and thus

removing it results in reduced damping ratio of the mode.

Fig. 3.11 (a) Eigenvalues of original system, (b) Eigenvalues of the system with inter-area mode

(Eigenvalues plot for positive frequencies near 0 only and the dashed line denotes 5% damping) and

(c) Mode shape of inter-area mode.


- 95 -

A comparison of the eigenvalues of the originally established dynamic GB system

and the modified version (PSS at bus 16 removed) is given in Fig. 3.11 (a) and (b).

The modified system has a pair of poorly damped inter-area oscillation modes

(-0.091±j3.04) with damping ratio of 3% and damped frequency of 0.48Hz. This

indicates that there is a low frequency inter-area oscillation which exists in the

network model involving two groups of generators swinging against each other. In

order to understand the coherency of the generators, a mode shape compass plot can

be used to illustrate the behaviour of the generators as it shows the relative activity

of the state variables in a particular mode. The normalized right eigenvector,

corresponding to rotor speeds of the generators in the system, of the inter-area mode,

is given in Fig. 3.11 (c) to show the grouping of generators in the inter-area

oscillation (mainly between G1-G4, G10 and the rest of the generators).

Time domain simulations show generator speed responses when the system is

subjected to a self-clearing 100ms three-phase fault at bus 10. This will cause a

maximum tie-line power oscillation of around 500MW. The speed responses of G1-

G5 in Scotland and G23-29 in England are illustrated by Fig. 3.12. The oscillation

takes more than 30s to damp and the figure is enlarged at the end, where the inter-

area oscillation is most obvious. The grouping of generators which have similar

behaviour can be observed. During the oscillation, when generators G1-G5 have a

decrease in speed, generators G23-G29, on the contrary, have an increase in speed

and vice-versa. The G2’s speed response has a half cycle period of 1.04s illustrating

the 0.483Hz inter-area low frequency oscillation in the developed system model, and

this validates the eigenvalue analysis provided before.

23.5 24.5 25.5

0.9996

0.9998

1

1.0002

1.0004

G1G2

G3

G4G5

G23-28

G29

1.04s

0 5 10 15 20 25 30

0.996

0.998

1

1.002

1.004

Time in seconds

Ge

ne

rato

r sp

ee

d in

p.u

.

Fig. 3.12 Generator speed responses during AC system fault event.


- 96 -

This characteristic GB system condition with the 0.483Hz inter-area oscillation

represents the incidents of the UK system in 1980 [85] where two groups of

generators in Scotland and England were oscillating against each other. This is used

as a base case of the GB system for stability studies in this thesis.

Heavily Stressed System

The system can be further pushed to its stability limits when it is heavily stressed.

To meet a particular pattern and level of demand, there are always choices about

which generators to use. This then affects the resulting load flow condition

throughout the system, and in some particular cases the system can be stressed. The

actual dispatch of generation will generally follow what is sometimes referred to as

"merit order", i.e. use the cheapest units first and keep committing units in turn.

These units are generally operated at maximum output, except those which require

'headroom' for primary reserve. These units have the priority to contribute first until

the total load demand and network losses are met. The power transfers across any

boundary would depend on exactly where these 'in merit' units are relative to the

individual loads. However, there are also uncertainties such as wind availabilities

and outages which also change the load flow pattern.

Thus, for a particular level of demand, the dispatch of generation can be modified.

As a consequence, the power flows from one region to another vary. One case that

can stress the system is to have a different dispatch of generation. Export of power

from Scotland could be very high under low demand (i.e. off peak) and high wind

conditions, in which a “merit order” dispatch of generation would favour low carbon

generation located in Scotland. However, to simplify this process, an alternative way

is to adjust the load demand to also change the power flow between the areas. For

example, the system can be stressed by considering all generation in Scotland as

being 'in merit'. Because Scotland would be a net exporting region, the highest level

of export would actually be under an off peak demand condition. The demand within

Scotland would be small in comparison to the total generation in the area, and hence

the power exported to England will be large. However, to be a credible situation,


- 97 -

there should not be any thermal branch overloads in the dispatch. Nonetheless, the

highest possible export without any overloads is likely to be a more suitable testing

case from a stability point of view.

More specifically, the system is stressed by increasing the generation in the Scotland

(Node 1-8) to their maximum available generation. Meanwhile, the load demand in

Scotland (Loads in Node 1-8) is reduced by a scaling factor x (x<1), and the reduced

load demand is uniformly added to the England network (Loads in Node 9-29).

Under such circumstances, more power will be transferred from the North to the

South, which will push the system towards its stability margin as illustrated in Table

3.8 and Fig. 3.13. It is observed that with an increasing amount of power transferred

from Scotland to England (as shown in the tie-line 8-10 power responses), the

system can result in oscillatory instability due to insufficient damping torque.

Table 3.8 Calculated inter-area mode when system is stressed.

Scaling Factor Inter-area mode

f in Hz Damping ratio

x=1 0.48 2.92%

x=0.9 0.48 2.07%

x=0.8 0.48 1.21%

x=0.7 0.47 0.35%

x=0.6 0.47 -0.49%

0.9

1

1.1

1.2

Bus2 V

in p

u

x factor=1

x factor=0.8

x factor=0.6

0 2 4 6 8 10 12 14 16 18 20500

1000

1500

2000

Time(s)

line 8

-10 P

in M

W

Fig. 3.13 System responses when stressed.


- 98 -

3.5. Shunt Device Dynamic Modelling

The SVC units installed in this GB system were initially modelled as constant

reactive power support to match the reference load flow scenario. However, for

dynamic studies, the SVCs need to be modelled in voltage control mode in response

to voltage variations in the system [86]. The SVC modelled in this case consists of

thyristor controlled reactors (TCRs) and thyristor switched capacitors (TSCs).

Ideally it should hold constant voltage by possessing unlimited VAr

generation/absorption capability instantaneously, as shown in Fig. 3.14.

Leading Lagging

V

IS

Ideal VI

characteristic

TCR TSC

IS

V

Fig. 3.14 SVC Model and ideal VI characteristic.

The basic structure of a TCR is a reactor in series with a bidirectional thyristor

switch [87]. Its partial conduction characteristic is determined by the firing angle α

that is in the range of 90°-180°. Firing angles between 0°-90° are not allowed as

they produce asymmetrical currents with a DC component. A TCR normally

responds in about 0.02-0.1s, taking into consideration delays introduced by

measurement and control circuits. On the other hand, the TSC scheme consists of a

capacitor bank split up into several similar sized units which can be switched in or

out of the scheme. An inductor is normally included to limit switching transients,

damp inrush current and prevent resonance with network. Although the control of

the TSC unit (by varying the number of TSC units in conduction) is discontinuous,

the voltage control of the SVC can be made continuous by using the TCR to smooth

out the variations in the effective susceptance.

The TCR and TSC schemes together form the SVC. The maximum compensating

current of a SVC decreases linearly with the AC system voltage, and the maximum


- 99 -

MVAr output decreases with the square of the voltage. The maximum transient

capacitive current is determined by the size of the capacitor and the magnitude of the

AC system voltage. In practical implementation, a droop characteristic [20] (a slope

value typically between 1-5%) is normally set for the SVC voltage regulation, as

shown in Fig. 3.15 (c). Within the linear control range, the SVC is equivalent to a

voltage source (Vref) in series with a reactance (e.g. XSL) which represents adjustable

admittance.

Two SVC control schemes are also illustrated in Fig. 3.15 (a) and (b). The first one,

Fig. 3.15 (a) utilizes a proportional type control with gain KR, which is the inverse of

the slope. Lead-lag blocks may be added to provide adequate phase and gain margin

when high steady-state gain is used. Alternatively, the droop characteristic may also

be configured through a current feedback as shown in Fig. 3.15 (b). The voltage

regulator can then be a PI controller type, and the controller gain and the slope

setting of SVC are independent from each other in this situation. Both controllers are

manipulating the susceptance of the SVC to control the compensation current.

Please see [87] for more detailed control settings.

V

Capacitive Inductive0

Current I

Kslope

1

1meas

sT

1

R

R

K

sT

Vref

VMeas

Bref

Auxiliary signalsVoltage Regulator

1

1

a

b

sT

sT

Lead Lag

Compensator

SVC

susceptance

control

1

1meas

sT

Vref

VMeas

Auxiliary signals

Voltage

Regulator

ISVS

SVC

susceptance

control ISVS

PI

1

R

R

K

sT

Current

Measure

(a)

(b) (c)

Fig. 3.15 Typical SVC control schemes.

An example of a SVC (-200MVAr capacitive to +50MVAr inductive) supplying a

SMIB system with the control scheme shown in Fig. 3.15 (a) is given in Fig. 3.16,


- 100 -

where the system is subjected to a 140ms three-phase fault at the SVC controlled

bus. A voltage drop and recover are seen during the fault at the SVC connected bus.

The SVC is injecting reactive power (capacitive) into the system during the fault,

attempting to hold the bus voltage by increasing its susceptance to its upper limit. It

then absorbs reactive power (inductive) from the system to bring the bus voltage

from the small overshoot back to 1 p.u. after the fault. Due to the characteristic of

the SVC, its reactive power capability is limited by its terminal bus voltage.

Therefore, it is not providing its rated reactive power during the AC system fault,

although it has reached its susceptance limits.

0 0.5 1 1.5 2-2

-1.5

-1

-0.5

0SG Rotor Angle

time(s)

An

gle

(rad

)

0 0.1 0.2 0.3 0.40

0.5

1

1.5SVC Voltage

time(s)

Bu

s V

olt

age

(p.u

.)

0 0.1 0.2 0.3 0.4

0

20

40

SVC Admittance

time(s)

Ad

mit

tan

ce(p

.u.)

0 0.1 0.2 0.3 0.4-60

-40

-20

0

20SVC Reactive Power

time(s)

Q(M

VA

r)

18/400kV

Transformer

SG

Load

Standard 192MW

CCGT Model

External

Grid

SVC

OHLs

Capacitive

Inductive

Fig. 3.16 Dynamic responses of SMIB system with SVC (negative Q is capacitive SVC operation).

The SVCs are modelled at appropriate locations for the dynamic GB system model

as specified in the reference case with the control schemes mentioned before. They

are supporting the voltage of their connected buses.


- 101 -

3.6. Light Loading GB System

Other loading conditions of the developed GB system can also be modelled by

properly scaling the existing load flow scenario. Future scenarios provided in the

National Grid ODIS show that the system will have a large proportion of renewable

generation. However, potential problems may occur when conventional generators

with large inertias (e.g. fossil coal, CCGT) are replaced by low inertia renewable

generators (e.g. offshore wind power) which are normally decoupled from the

system by power converters. In order to address this, a test system condition with

such features can be established. This section shows the method of modifying the

system into a lightly loaded condition (e.g. summer time light loading) system with

large wind power penetration.

According to the summary from National Grid, the “Total Gross System Demand” is

used to determine the total amount of load demand at different times of a year. This

is calculated from [73] generation data which includes station load, pump storage

and interconnector exports. The minimum loading condition can be estimated based

on such data. The main procedures for developing a light loading system are

summarized as:

i. All the fossil generation units are closed in the system, and the nuclear

generation units in the Scotland part are closed (i.e. G4, G5, G7, G15, G17,

G18 and G23 are disconnected from the system). These units are considered as

conventional generation which will be replaced by renewable generation.

ii. More windfarm injections are added into the system as suggested in ODIS.

Specifically, windfarms are modelled at bus 2 (1GW), bus 5 (2GW), bus 7

(2GW), bus 12 (1GW), bus 19 (2GW) and bus 26 (1GW) as suggested by the

planned Round 3 windfarms. In total this introduces 9GW wind power

injection into the system. The original generation at those buses is considered

to be replaced by windfarm generation, and thus the original generation is

disconnected from the system. For practical implementation of wind power

grid connection, there may be reactive power compensation devices installed


- 102 -

at the grid entry point for windfarms, and thus SVC with appropriate reactive

power capability may be modelled along with the added windfarms [88].

iii. In order to reach a light loading condition based on the data in [73], CCGT

generation units are scaled down to reach a total system generation of around

25GW. All the system loads are also scaled down accordingly to match the

new generation. The power of all remaining generation in the system as well

as the interconnectors remains unchanged.

The above modifications would result in a light loading system with a total

generation of 25GW which represents the future summer minimum demand

condition of the developed AC system model with a large proportion (circa 40%) of

wind power penetration. Table 3.9 provides the summary of the resulting generation

of different loading conditions, where the total windfarm generation is increased

from 0.87GW to 9.85GW. Hydro and nuclear type generators are maintained due to

their inflexibility. A dramatic decrease is seen for CCGT type generation (from

2.81GW to 0.5GW). Modal analysis of the light loading condition system shows that

the system is well damped, with all the system modes damping ratios above 10%.

There are no inter-area modes in this case when the load demand is largely reduced.

Table 3.9 Summary of generation in different loading conditions.

Generation Type Generation for heavy

loading (MW)

Generation for light

loading (MW)

Hydro 1634.00 1634.00

CCGT 28111.00 4961.00

Wind 871.00 9845.00

Nuclear 11545.00 8237.76

Coal 18180.64 0.00

Total Generation 60341.64 24677.75

To compare the dynamic performance of the developed heavy and light loading

conditions of the system, time domain simulations are performed. In this case, the

system is disturbed by two typical events: (1) AC system three-phase fault event and

(2) variations in load demand. In this case, the focus is put on system voltage and

frequency responses in order to investigate the differences between the two loading

conditions of the system in respect of the voltage and frequency controllability. The


- 103 -

comparison is made between the buses with the largest voltage/frequency deviations.

Such buses are selected by observing and comparing the voltage/frequency

responses of all system buses during an event. The comparison of the resulting

voltage and frequency responses of the selected buses in two different loading

conditions are given in Fig. 3.17 and Fig. 3.18. As the conventional generation with

slow DC1A exciters is closed in the light loading condition, its voltage control is

largely determined by the fast ST1A exciters. A large portion of generation is

provided by the windfarms with constant power factor control. These windfarms

behave in a similar manner to active loads in the system. Therefore, for the three-

phase fault event, system voltages converge very quickly with less oscillation in the

lightly loaded condition. However, the largest amount of voltage deviation right

after the fault is almost the same for both cases. The frequency responses of both

system conditions for the AC fault event are also very similar.

Fig. 3.17 Bus 2 voltage and bus 29 frequency responses for a 100ms self-clearing three-phase short

circuit event at bus 24.

As governors are not included in the model for this case, the load ramp event causes

a power mismatch in the system (loading>generation). Under such circumstance, the

system frequency starts to decrease. Comparison in Fig. 3.18 shows a more rapid

frequency decrease initially with the heavy loading condition rather than the light

loading condition. This is because the rate of change of frequency in the initial stage


- 104 -

depends not only on the system inertia but also the amount of power mismatch in the

system. After the initial stage, the light loading condition has a faster frequency

decrease rate. Nevertheless, the light loading condition has faster voltage control.

Fig. 3.18 Bus 2 voltage and frequency responses for 1GW ramp up change in 2s in load 25

3.7. Conclusion

In this chapter a dynamic “representative GB system” is developed, based on a

realistic reference case. A detailed road map of the key procedures for the dynamic

construction of the system is provided together with all the necessary system data

required to reconstruct such a system. This mainly includes the methods used for

generator dynamic parameters selection, controller design and system condition

adjustment to finally achieve a system model with particular characteristic features.

The developed system is modified for different system conditions. These system

conditions are useful depending on the particular focus of one’s subject of research.

One of the system conditions has the characteristic of a low frequency inter-area

oscillation with most of the generators in the system participating. Such a

phenomenon is demonstrated using both small disturbance analysis and time domain

simulations. This is mainly caused by the generators in the Scottish part (G1-G4)


- 105 -

oscillating against the generators in England, with a damping ratio less than 5%.

More stressed system conditions are also discussed where the inter-area oscillation

becomes more obvious and the system can be pushed beyond its stability margin.

Additionally, a light loading system condition is also developed, which has

improved the system voltage control capability due to the remaining fast exciters in

the system. However, frequency control in such a system condition becomes more

challenging as the total system inertia is reduced.

As the developed model provides a dynamic equivalent representation of a GB

transmission network, further analysis on AC/DC interactions can be carried out

based on this network model. The use of this more realistic large power system

model helps to ensure that the results obtained are representative of practical system

implementations.

Chapter 4. The Effect of VSC HVDC Control

- 106 -


Chapter 4. The Effect of VSC HVDC Control on

AC System Electromechanical Oscillations and

DC System Dynamics

The operating point and the control strategies employed in VSC based HVDC systems

can substantially affect the electromechanical oscillatory behaviour of the AC network

as well as the DC side dynamics. In order that the full, flexible capability of VSC HVDC

can be exploited, the study of the effects of these controllers and their interactions with

AC system responses is necessary. This chapter provides a full assessment of the effect

of VSC controls in a point-to-point DC link and a four-terminal DC system. Both modal

analysis and transient stability analysis are used to highlight trade-offs between

candidate VSC outer controls and to study the electromechanical performance of the

integrated AC/DC model. Tests are carried out with both the two-area system model

and the dynamic GB system model.

4.1. Methodology for VSC Control Assessment

VSCs have complex hierarchical control structures. A variety of these has been

proposed and analysed [11, 31, 34, 38, 53, 59, 61-63, 67, 69], but the focus has been the

delivery of required performance on the DC side and within the converter rather than

the interaction with the AC system. The AC system has thus not been modelled in detail

in these cases. Conclusions have been reached about the efficacy of droop control [61,

67] used in multi-terminal DC grids and supplementary power oscillation damping

(POD) controllers [33, 34]. AC system studies have also been undertaken, but the focus


- 107 -

has been on the AC system dynamics — the VSC HVDC system and controllers have

typically been severely abstracted [30, 33, 34]. A holistic approach needs to be taken

which utilizes a detailed AC/DC modelling methodology and control designs to

systematically compare candidate VSC HVDC controllers.

In this chapter the VSC outer power and voltage controls are analysed. Taking into

considerations of the control loop bandwidth (from a few Hz to tens of Hz), the

methodology used to compare these controls is to study: (1) the control effects on AC

system inter-area oscillation and (2) the control effects on DC system dynamic

responses. The analysis is focused on the case of a point-to-point DC link embedded

within each of two test AC systems. One is the two-area system designed for inter-area

electromechanical oscillation analysis [20]. This facilitates the analysis of the effects of

VSC HVDC without being obscured by complex AC system structures. The second AC

test network is the dynamic GB system developed in Chapter 3, with the intention of

validating using more realistic system parameters. The use of the large power system

model with realistic constraints and reinforcement strategies facilitates the practicality

of the studies carried out and the generalization of conclusions.

4.2. Control Parameterization

The control system for VSC has a hierarchical cascaded structure which can be

classified into three levels, as shown in Fig. 4.11, with bandwidth separation. In this case,

the outer controllers (L2) will be focused on and analysed. The fast inner loop (L1)

includes the DC to AC voltage conversion and a decoupled vector current control (dq

current control). A phase locked loop (PLL) is employed to lock on to the point of

common coupling (PCC) voltage and to provide the reference angle for the VSC. The

typical VSC outer control schemes that fall into the category of L2 are listed in Table

4.1. For convenience, the abbreviations in Table 4.1 are used in the rest of this chapter.

1Fig. 4.1 is reproduced here for convenience. Detailed descriptions for the cascaded controls are available

in Chapter 2.


- 108 -

XcouplingTc

vabc eabciabc

Vdc

Ceq

abc / dq

PLL

id*

id

PIud ed

vd

vdq, idq

iq*

iq

uq eq

vq

PI

L

Decoupling Term

dq / abc

X

PIX*

P*,Q*

ND

N

D vd

idq_max

idq_min

FB type with

X = Vdc,Vac, P,Q

FF type

Kdroop

Referenc

es set

points

L1: Voltage and dq current loopL2: Outer control loops

L3:

Supervisory

control loops

idcic

AC System

PCC bus sV 0

Rs+jXs

Tele-

communication

Fig. 4.1 Full diagram of VSC terminal model and control structure.

Table 4.1 VSC outer controls and abbreviations.

VSC typical outer control schemes Abbreviations

Feedback (FB) DC voltage control FBVdc

Feedforward (FF) real and reactive power control FFP and FFQ

Feedback real and reactive power control FBP and FBQ

Feedback AC voltage control FBVac

The closed-loop bandwidth of the VSC outer control loops refers to the frequency

where the magnitude of the response is equal to -3dB. Normally, the bandwidth falls

into the range of a few Hz to tens of Hz (e.g. 1-20Hz). It is therefore possible for these

controllers to influence the electromechanical behaviours of the connected AC system.

In this section, the parameterization of these outer controllers is discussed. To undertake

this task, it is assumed that the inner current loops are fast enough to be simplified as

constant gains, and the AC system dynamics are considered as infinite buses. The

notations defined in Fig. 4.1 are used here.

With power invariant dq transformation and the assumption that the rotating reference

frame is aligned to the d-axis, the VSC output power at the PCC bus can be expressed

as:

d d q q d dp v i v i v i (4.1)


- 109 -

q d d q d qq v i v i v i (4.2)

where vdq and idq are the voltages and currents at the PCC bus. These equations are used

by FFP and FFQ, which relate directly the real and reactive power orders to dq current

orders, and therefore no additional outer controllers are introduced. The block diagram

representations of the feedforward type PQ controls are presented in Fig. 4.2.

P*

vd

id*

current

loop

idvdo

P

vqiq

Q*

-vd

iq*

current

loop

iq-vdo

Q

vqid

N

D

N

D

Fig. 4.2 VSC FF type control block diagram representations.

Droop control adds an additional gain to the FF or FB power loops, and sets the

allowable DC voltage variations for given power limitations. To cover the typical droop

gains, the range of 1<kdroop ≤ 30 will be considered [61]. With respect to the four FB

type outer control loops with additional PI controllers (i.e. FBVdc, FBP, FBQ, FBVac),

the parameter settings can be determined by means of frequency responses of closed-

loop transfer functions.

Modelling of Feedback DC Voltage Loop

The dynamics of the FBVdc controller are dominated by the DC side capacitor, and they

are expressed as:

dc d d

eq c dc dc

dc

dV v iC i i i

dt V (4.3)

Linearizing gives:

2

dc do do do doeq dc d d dc

dco dco dco

dV v i v iC V i v i

dt V V V (4.4)


- 110 -

where a subscript ‘o’ represents the operating point value. Based on the above equation,

the closed control loop can be represented by Fig. 4.3 (a). Let KV=vdo/Vdco and

KG=ido/Vdco, the closed-loop transfer function is expressed as:

* 2 ( )

pdc V idc Vdc

dc eq V G pdc V idc V

k K s k KV

V C s K K k K s k K

(4.5)

This equation can be further approximated to a second order transfer function (assuming

kpdc≪ kidc) as:

2

* 2 22

( ) 2

idc V

eqdc n

V G pdc idc Vdc dc n n

eq eq

k K

CV

K K k k KV s ss s

C C

(4.6)

This allows an approximation of an initial tuning value for the controller for a given

natural undamped frequency ωn and damping ratio ξdc.

idcpdc

kk

s

Vdc*

Vdc

id*

current

loop

id

do d

dco

i v

V

dcoi2

2

dco

do do dco eq

V

v i V C s

dcV

Q

Q

kikp

s

Q*

Q

iq*

current

loop

iq-vdo

Q

kiackpac

s

v*

v

iq*

current

loop

iq

Xsv

-1

Rsido

do

dco

v

V

cossV

vqid

(a)

(c)

(d)

PP

kikp

s

P*

P

id*

current

loop

idvdo

Pvqiq

(b)

Fig. 4.3 VSC FB type control block diagram representations.


- 111 -

Modelling of Feedback Real and Reactive Loops

Based on equations (4.1) and (4.2), the closed FB real and reactive power control loops

can be defined as Fig. 4.3 (b) and (c). Ignoring the disturbance terms, the plant model

for both real and reactive power is mainly determined by the operating point PCC

voltage ±vdo, which can be represented by a gain g at an operating point. Then the

closed-loop transfer function for both FBP and FBQ takes the form of a first order

transfer function as (assuming kpPQ≪ kiPQ):

( )*

pPQ iPQ iPQ

do

pPQ iPQ iPQ

gk s k kxg v

x s gk s k s k

(4.7)

where x can be either P or Q. The target bandwidth can be initially approximated by kiPQ.

Modelling of Feedback AC Voltage Loop

For the FB type AC voltage control, the closed-loop transfer function derivation is

slightly more involved. Assuming an infinite AC bus with voltage Vs∠0° (Fig. 4.1),

after dq transformation, the following equation was established:

( ) ( ) ( )( )d q sd sq s s d qv jv V jV R jX i ji (4.8)

Solving gives:

d sd s d s q

q sq s q s d

v V R i X i

v V R i X i

(4.9)

For an ideal PLL, the PLL angle varies with the PCC bus voltage angle, and so are all

other system parameters in the dq domain. The infinite bus voltage Vs∠0° in the dq

domain is:

cos sin

sin cos

sd sr

sq si

V V

V V

(4.10)

where Vsi=0 and Vsr = Vs. Angle θ is the PLL angle.

With equations (4.9) and (4.10), and the rotating reference frame being aligned with the

d-axis (i.e. vq=0), the PCC bus voltage is now given as:

2 2 cosd q d s s d s qv v v v V R i X i (4.11)


- 112 -

The closed-loop transfer function for FBVac can then be expressed as Fig. 4.3 (d) which

is disturbed by Rsido (related to the operating point of the DC link) and Vscosθ. The

closed-loop transfer function is, however, similar to equation (4.7), where the

bandwidth can be initially approximated by kiac.

The above simplified control closed-loop transfer functions of the four FB type controls

allow quick tuning of the controllers, after the initial approximation, to achieve a given

closed-loop bandwidth. More accurate controller parameters can be further set by

examining the frequency responses of the closed-loop transfer functions via Matlab

software (Matlab pidtool) with the tuning techniques outlined in [89]. For each FB type

control loop, a set of parameters is tuned for the outer controllers to cover their typical

bandwidth range in preparation for comparison purposes in the later stages. Fig. 4.4

shows an example of the feedback real power control closed-loop frequency response

after it is tuned to a bandwidth of 5Hz.

-60

-40

-20

0

From: Pref To: VSC2/Fcn2/P

Ma

gn

itu

de

(d

B)

100

101

102

103

104

-135

-90

-45

0

Ph

ase

(d

eg

)

P control close loop frequency response

Frequency (rad/s)

-3dB,5Hz

kp=0, ki=31.4

Fig. 4.4 Example of closed-loop frequency responses.

4.3. Method of Analysis

The influence brought by the control strategies on the AC and DC side of the system is

investigated separately with different methodologies.

Effects on AC System

From the perspective of the AC side, the investigation focuses on the impact of VSC

HVDC link on inter-area electromechanical modes in the AC system. In order to


- 113 -

identify the critical oscillatory modes, the eigenvalues of the system with frequencies in

the range of 0.2 to 1 Hz need to be scanned. Two modal analysis techniques are used: (1)

the QR method [90], which is robust for small power systems, and (2) the Arnoldi

method [91], which can be implemented with sparsity techniques to calculate a specific

set of eigenvalues with certain features of interest (e.g. the low frequency inter-area

modes in this case). The Arnoldi method is considered efficient to solve partial

eigenvalues for large integrated AC/DC systems. The application of this sparsity based

eigenvalue technique to the small disturbance stability analysis of a large power system

was presented in [92]. The detailed critical mode tracking procedure is illustrated by Fig.

4.5 which shows an iterative process. One controller will be varied while all the other

controllers in the DC link remain the settings of a based case. Targeting at low

frequencies, the inter-area mode can be tracked.

As AC system inter-area oscillations are complex and involve a large number of

generators, a generic small two-area system with a characteristic inter-area mode is

firstly investigated. The QR method is used to track the critical oscillatory mode for this

small system. The key findings are then tested with the larger and more realistic

representative GB system, where the Arnoldi method is applied for inter-area mode

monitoring.

Select outer

controller

Increase controller

bandwidth

Modal analysis of

AC/DC system

Track low frequency

inter-area mode

Fig. 4.5 Eigenvalue tracking procedure.

Effects on DC System

The dynamic responses on the DC side of the system are much faster than those on the

AC side. Hence the effects of VSC controls on the DC system are less influenced by the

AC side dynamics and they are better shown by DC side transient responses. Therefore,

the controls are compared by monitoring the dynamic responses of DC system


- 114 -

parameters. Different controller parameter settings, based on the tuning procedures

discussed before, are applied to provide a sensitivity analysis showing the resulting

system behaviours. The main focus of this research is on normal operating conditions,

and thus the test conditions modelled do not cause control limiters to be activated.

4.4. Investigation Based on Generic AC System

The classical two-area AC system developed before is firstly used in these studies. This

detailed system model is described in Chapter 2 and the system diagram is again

presented in Fig. 4.6. This is a detailed integrated AC/DC system with sixth order

generator models, and VSC models employing control schemes shown in Fig. 4.1.

In the following studies, the term “fast” and “slow” controls will be used to represent a

FB type control which is tuned with a bandwidth of 30Hz and 1Hz respectively. The

purpose of this is to push a particular controller to its parameter setting limits to show

the corresponding effects under certain conditions.

VSC HVDC link

R+L

PCC2PCC1

CeqCeq

G1

G2 G3

G4

25km 10km

110km 110km

1 5

2 3

46

7

8

9

10 11

Two-area

AC network

AC tie-lines

Area1 Area2

VSC1 VSC2

Vdc1 Vdc2idc

R+L

idc1 idc1

RdcLdc

Fig. 4.6 Generic two-area system with embedded VSC HVDC link.

Effects of VSC Outer Controls on Inter-area Mode

The idea here is to investigate the AC system inter-area oscillation under the effect of

different VSC outer control schemes and operating points. Specifically, the AC system


- 115 -

low frequency inter-area mode is monitored by applying QR method to the whole

system matrix with different VSC HVDC configurations. However, for FB type

controllers, as they can be configured differently depending on the outer controller, the

investigation of their effects needs to cover their typical settings. This is achieved by

including a bandwidth sensitivity analysis for each of these FB controls detailed in test

case 2.

Test Case 1: Comparison of FF and FB Type Controls

Two control scenarios are listed in Table 4.2, where FBVdc is configured to a bandwidth

of 10Hz in both cases. The FF type PQ controls in Scenario 1, which do not require

additional controllers, are examined first. The QR method is applied to obtain the inter-

area mode for different power flow conditions in the DC link. The resulting inter-area

mode frequencies (f) and damping ratios (ξ) are listed in Table 4.3. All the FF type PQ

controls in Scenario 1 are then replaced by FB type PQ controls (Scenario 2) with

identical bandwidths. The same test now yields results shown in Table 4.4.

Table 4.2 VSC control settings case 1.

Control Scenarios VSC1 VSC2

Scenario 1 FBVdc FFQ FFP FFQ

Scenario 2 FBVdc FBQ FBP FBQ

Table 4.3 Inter-area mode tracking with FF type controls.

DC link power Inter-area mode

f Hz ξ %

50MW 0.56Hz 3.82%

150MW 0.56Hz 4.54%

250MW 0.56Hz 5.25%

350MW 0.55Hz 5.86%

Table 4.4 Inter-area mode tracking with FB type controls.

DC power

Inter-area mode

Slow FB controls Fast FB controls

f Hz ξ % Frequency ξ %

50MW 0.56Hz 3.45 0.57Hz 3.48

150MW 0.58Hz 3.32 0.58Hz 3.36

250MW 0.58Hz 3.07 0.58Hz 3.10

350MW 0.57Hz 2.66 0.57Hz 2.66


- 116 -

2 4 6 8 10 12 14 16 18

0

200

400

P in

MW

Time(s)

50MW DC power

350MW DC power

0

200

400

P in

MW VSCs with FF type PQ controls

VSCs with FB type PQ controls

Fig. 4.7 Tie-line power responses at different operating points.

Originally, without the embedded DC link, the two-area system has an inter-area mode

of f=0.545Hz and ξ=3.2% [20]. According to the results in Table 4.3, it is seen that the

inter-area mode damping ratio increases with the DC link power when FF type PQ

controls are employed. In contrast, adding the DC link with FB type PQ controls (Table

4.4), the inter-area mode damping ratio decreases with the DC link power. In both cases

the frequency of the mode remains largely the same. A faster or slower FB type PQ

controller does not influence significantly the inter-area mode. This is validated by a

time domain simulation in Fig. 4.7, which compares the tie-line power responses for

both scenarios with different DC link powers following a three-phase 100ms self-

clearing fault at bus 5.

Test Case 2: Effects of Individual FB Type Controls

Case 2 focuses on individual FB type control schemes. In setting up the comparison of

various control parameters in this case study, a reference base case is firstly defined.

The DC link is now configured with a control strategy specified in Table 4.5, i.e. all the

FB control loops are tuned to have a bandwidth of 5Hz, except FBVdc that is tuned to

10Hz. This serves as the reference base case, so that the resulting closed-loop step

responses for these FB type controls have no significant overshoot, a 10%-90% rise

time of 0.1s and no steady-state error.

Table 4.5 VSC control settings case 2.

VSC1 VSC2

FBVdc FBQ/FBVac FBP FBQ/FBVac


- 117 -

The FBQ in VSC2 was changed to FBVac when analysing the effect of AC voltage

control. The procedure of the bandwidth sensitivity analysis is a set of iterative

processes where one controller will be varied with different bandwidths by adjusting the

outer loop PI controller each time, while all the other controllers in the DC link remain

at the settings of the reference case. In this case, one outer controller – FBVdc in VSC1,

FBP, FBQ or FBVac in VSC2 – is varied for testing. For two DC link operating points,

the root loci of the inter-area mode, which is affected by different control settings, are

plotted in Fig. 4.8 (a) and (b) with arrows indicating the directions of increasing

controller bandwidth. The bandwidths of the controllers here are pushed to a larger

range (1-30Hz) to more clearly show the movement of the inter-area mode.

-1 0 1 2 3 40.54

0.56

0.575

Damping Ratio %

Da

mp

ed

Fre

qu

en

cy (

Hz)

7HzVac Control 1-30Hz

StableUnstable

3.14 3.41

0.571-30Hz

P Control

Vdc Control

Q Control

1 1.5 2 2.5 3

0.56

0.565

0.57

0.575

Damping Ratio %

Da

mp

ed

Fre

qu

en

cy (

Hz)

Vac Control 1-30Hz

Stable

2.8 3.2

0.58

P Control

Vdc Control

Q Control

1-30Hz

Fig. 4.8 Root loci of inter-area mode with bandwidth variations in individual FB type control loop at (a)

100MW DC link power and (b) 200MW DC link power.

(a)

(b)


- 118 -

The results, illustrated by Fig. 4.8 (a) and (b) for 100MW and 200MW DC link power

flow conditions respectively, lead to the following conclusions:

2a. The inter-area mode damping ratio increases with the bandwidth of FBVdc, FBP

and FBQ. However, such an impact is very small in comparison to the effect of

the bandwidth variations in FBVac.

2b. FBQ has a larger impact on the inter-area mode damping ratio and frequency

when the DC link power operating point is higher.

2c. The inter-area mode damping deteriorates as the bandwidth is increased for

FBVac in VSC2. This is particularly true for the case of 100MW DC link power,

when the damping ratio of the inter-area mode is pushed to a negative value with

a FBVac of bandwidth 7Hz. In such a case, the system will become unstable.

2d. The frequency of the inter-area mode is decreased when FBVac is employed in

VSC2 instead of FBQ. However, variations in FBVac control settings have little

impact on the inter-area mode frequency.

Test Case 3: Further Investigation on FBVac

Since it has been identified in test case 2 that the bandwidth of the AC voltage

controller has the largest influence on the inter-area mode compared with all other FB

type controls, this test case is chosen for further analysis in this section.

It can be observed from the two plots in Fig. 4.8 that with higher DC link operating

conditions, FBVac has decreasing influence on the damping ratio but increasing

influence on the frequency of the inter-area mode. This is more clearly shown in Fig.

4.9, which compares the inter-area mode movement affected by FBVac (bandwidth=1-

30Hz) with respect to different DC link operating points. Other tests show that the effect

of FBVac on the damping of inter-area mode also depends on its location. This is

demonstrated in Fig. 4.10 by comparing the effect of FBVac (bandwidth=1-30Hz) in

VSC1 (sending end) and VSC2 (receiving end) of 100MW DC link power.


- 119 -

-1 1 3 40.54

0.56

0.58

Damping Ratio %

Dam

ped

Fre

quen

cy (

Hz) 300MW DC Link

Power

100MW DC Link Power

200MW DC Link Power

0

Unstable Stable

Vac Control 1-30Hz

2

Fig. 4.9 Root loci of the inter-area mode for FBVac control.

-1 0 1 2 3 4 50.54

0.56

0.58

0.6

0.62

Damping Ratio %

Dam

ped

Fre

qu

ency

(H

z) Vac Control in VSC1

1-30Hz

Vac Control in VSC21-30Hz

Fig. 4.10 Root loci of the inter-area mode with FBVac at different locations (DC link power =100MW).

The effect of FBVac in VSC terminals on inter-area mode is comparable to the effect of

fast exciters in the synchronous generators [93]. Continuing with the conclusions in the

previous test cases, some characteristics of the FBVac can be summarized as:

3a. With an increasing DC link power, the impact of FBVac on the damping ratio of

the inter-area mode decreases while the impact on the frequency of the inter-area

mode increases as shown in Fig. 4.9.

3b. The location of the FBVac has a strong impact on the damping ratio of the inter-

area mode, which is similar to the effect of one fast exciter in one of the four

generators stated in [93]. A fast FBVac at the receiving area (VSC2) reduces the

damping of the inter-area mode, while one at the sending area (VSC1) improves


- 120 -

the damping (Fig. 4.10). This general behaviour agrees to a certain extent with

the case of one fast exciter and three slow exciters in the four generator test

system of [93]. However, in [93], it is stated that in the case of one fast exciter

and three manually controlled exciters, a fast exciter in the receiving area

improves the damping while one in the sending area reduces the damping. This

is not the case with FBVac as further tests showed that the effect of the location

of FBVac does not change when the slow exciters in the generators are replaced

by manually controlled exciters.

3c. The impact of the location of FBVac on the frequency of the inter-area mode is

similar to the effect of one fast exciter in one of the generators [93]: A fast FBVac

or exciter in the sending area increases the frequency of the mode, while one in

the receiving area reduces it.

The effect of FBVac is validated by time domain simulations presented in Fig. 4.11,

which compares the tie-line power responses for a three-phase 100ms self-clearing fault

at bus5 considering different configurations of FBVac.

FBVac of 1Hz

FBVac employed in VSC1


0

50

100

150

200

250

300

0 2 4 6 8 10

tie

line

pow

er in

MW

Time(s)

0

50

100

150

200

250

300

0 2 4 6 8 10

tie

line

pow

er in

MW

Time(s)

FBVac of 7Hz

1.69s

f = 0.6Hz

1.92s

f = 0.52Hz

Fig. 4.11 Effect of FBVac control in different locations (DC link power =100MW).

Tests regarding the effect of droop gain settings on the inter-area mode are also carried

out. However, in the case of a point-to-point DC link, different droop gains added to


- 121 -

either FF or FB type outer controllers result in very similar inter-area mode behaviour

as the cases without adding the droop gain. Therefore these results have been omitted

for brevity.

DC System Effects

The effects of VSC controls on the DC side system are reviewed by means of sensitivity

analysis based on a set of simulated comparisons. In this case, the focus is put on the

dynamic behaviours of the DC side voltage and the DC link real and reactive power

output when they are affected by different VSC controls. The dynamic performance of

the control schemes is compared for both parameter step change events and the three-

phase fault (same type and location of the fault as before). The results are presented in

Fig. 4.12 where (a)-(d) show the step responses and (e)-(h) show the AC fault responses.

From this comparison, the following conclusions can be drawn:

DC side voltage

The dynamic behaviour of DC link voltage is mainly affected by FBVdc or droop control.

Other controls show limited impact on the DC voltage responses. Effects of FBVdc

configuration are illustrated by Fig. 4.12 (a) and Fig. 4.12 (e).

The effect of droop gain is shown in Fig. 4.12 (b) and Fig. 4.12 (f). As the DC line

impedance is not very large, even though different droop gain settings are applied in

each case to both VSC1 and VSC2, the initial and resulting DC voltage values are

almost the same for the different droop gain values. Steady-state error is seen with

droop control for step changes. Larger droop gain results in slightly smaller DC voltage

oscillations following the AC fault. A comparison of FBVdc (bandwidth=10Hz) and

droop control with droop gain of 10 cascaded on a FBP with bandwidth=10Hz is given

in Fig. 4.13, where droop control gives better voltage control under the AC fault.

Real Power and Reactive Power

The DC link real and reactive power outputs are mainly affected by VSC PQ controls.

This is illustrated by Fig. 4.12 (c) and Fig. 4.12 (g) for real power responses and Fig.

4.12 (d) and Fig. 4.12 (h) for reactive power responses.


- 122 -

Note that, in Fig. 4.12 (h), during the AC system fault, FFQ results in large oscillations.

This is due to the errors in PLL causing vq to be non-zero during an AC system fault,

and thus the disturbance terms vqiq and vqid in Fig. 4.2 and Fig. 4.3 are no longer zero.

However, as vqiq (iq≈0) is much smaller than vqid, larger oscillations appear with FFQ

control for the AC system fault event. To analyse this further, the disturbance terms also

affect FF and FB type PQ control differently during the AC system fault event.

Assuming an ideal inner current loop and vq to be non-zero after an AC fault, according

to the block diagram transfer functions shown before, we have:

FF type PQ control:

* *

do q q do q d

d d

P Qv v i P , v v i Q

v v

(4.12)

FB type PQ control:

* P do P do

q q

P do P do P do P do

skp v ki v sP v i P

s kp v 1 ki v s kp v 1 ki v

(4.13)

Q do Q do*

q d

Q do Q do Q do Q do

skp v ki v sQ v i Q

s 1 kp v ki v s 1 kp v ki v

(4.14)

It can be observed from the above equations that the disturbance terms vqiq and vqid

affect FF type control output power directly during the AC system fault event. However,

they are attenuated in the case of FB type control by the outer controller. This is because

FF type PQ control relies on the assumption that P = vdid and Q = -vdiq which requires a

correct operation of the PLL and is not able to “see” variations in vq. FB type PQ

controls are based on the fuller power equations, and thus they are able to modify their

current references when the disturbance terms vary. A more comprehensive comparison

of FF and FB type PQ controls is addressed in [57].


- 123 -

0.9 1 1.1 1.2 1.31

1.05

1.1

1.15

time(s)

Vd

c1

in

p.u

.

1 1.05 1.1 1.15 1.2

100

120

140

160

180

200

time in s

P in

MW

1 1.05 1.1 1.150

20

40

60

80

100

120

time in s

Q in

MV

ar

1 1.1 1.2 1.3 1.4

1

1.02

1.04

1.06

time in s

Vd

c1

in

p.u

.

(a) Time(s) (b)

10 1Hz

30 1Hz

10 0.6Hz

5droopk

15droopk

Step Reference 1 to 1.05

FFP

FBP 5Hz

FPB 15Hz

FFQ

FBQ 5Hz

FBQ 15Hz

Ste

p r

esp

on

ses

FBVdcDroop with FBVdc 10 1Hz

(c) Time(s) (d)

0.8 1 1.2 1.4 1.60.9

0.95

1

1.05

1.1

1.15

time(s)

Vd

c1

in

p.u

.

1 1.1 1.2 1.3 1.40.98

0.99

1

1.01

1.02

1.03

time in s

Vd

c1

in

p.u

.

1 1.2 1.4 1.6 1.8 2

90

95

100

105

110

time in s

P in

MW

1 2 3 4 5-10

-5

0

5

10

15

time in s

Q in

MV

ar

10 1Hz

30 1Hz

10 0.6Hz

5droopk

15droopk

FBP 5Hz

FBP 15Hz

FFP

FFQFBQ 5Hz

FBQ 15Hz

(e) Time(s) (f)

AC

sy

stem

fau

lt r

esp

on

ses

FBVdc Droop with FBVdc 10 1Hz

(g) Time(s) (h)

Fig. 4.12 DC side dynamic response comparison of different control schemes for step change (a-d) and

AC system fault (e-h) events.


- 124 -

1 1.2 1.4 1.6 1.8 2

0.98

1

1.02

time in s

Vd

c1

in

p.u

.

FBVdc of 10Hz

Droop control with kdroop=10

Time(s)

Fig. 4.13 Comparison of constant Vdc and droop control.

4.5. Test Based on Dynamic GB System

In this section, the test AC system is replaced by the dynamic GB system developed in

Chapter 3 and shown in Fig. 4.14. The identifications based on the generic two-area

system are further tested.

27

26

2829 C

NN C

1 2

C

H

3

F

4

5

N 6

WF

7

8N

9 10

C11

N

15

F

12

13 14

C

16

C

1917

C

2022

21N

C

C

F

18

F

23

24

25

F C

H

VSC1

VS

C2

DC

ca

ble

Phase

Reactor

Hydro

OHL

Bus

Transformer

Load

& Shunt

H

C

N

F

WF

CCGT

Nuclear

Fossil

Wind

Farm

Main Direction of

Power FlowNorth

Fig. 4.14 “Dynamic GB system” with embedded VSC HVDC link.


- 125 -

In this case study, all generating units utilize the detailed sixth order synchronous

generator model, except the wind generator which is modelled as a windfarm connected

through a converter to the grid. Standard IEEE exciters are used for different generation

types, and the designed PSSs are equipped. Governors are not included for this study as

only electromechanical transients are of interest. A number of circumstances (e.g.

different dispatch of generations, different loadings etc.) may cause problems in such a

system. To illustrate this, the system is further stressed by adjusting the distribution of

the load in different areas, creating a situation where more power is transferred from the

North to the South without any thermal branch overloads. This represents the situation

where Scotland is exporting power for the heavy load demand in the England network,

which will push the system to reach its stability margin.

For a heavily stressed condition, the system model has a 0.47 Hz low frequency inter-

area electromechanical mode [94]. Fig. 4.15 highlights this unstable eigenvalue with

damping ratio of -0.5%.

-1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 00

2

4

6

8

10

12

140.05

Real

Ima

gin

ary

System with inter-area modes

0

damping

ratio of 5%

0.5% 0.47f Hz

90

G1-G4, G10

G5,G7, G11-29

Inter-area mode

shape plot

System with inter-area modes

2

4

10

12

14

8

6

Imag

inar

y

-1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0Real

0

Fig. 4.15 Eigenvalues of the stressed dynamic GB system (eigenvalues with small negative parts and

positive frequencies only) and mode shape plot.

The normalized right eigenvector of inter-area mode, corresponding to rotor speeds, is

also given in Fig. 4.15 to show the grouping of generators in inter-area oscillation

(mainly between G1-G4 and the rest of the generators). Based on the mode shape plot,


- 126 -

an embedded VSC HVDC link is modelled, between bus 4 and 14, to connect the two

generator groups. This represents a future eastern link proposed for the GB grid [95].

The power is transferred in the direction from VSC1 to VSC2 (North to South) with a

total installed capacity of 1GW. The DC cables of approximately 400km are modelled

using four lumped equivalent π sections for each one.

There are in total more than 230 state variables in this integrated system, including

mainly the states in the synchronous generator models and controls, as well as the states

in the VSC HVDC converters and controls. Due to the size of the whole integrated

system, it is considered efficient to only calculate a specific set of eigenvalues with

certain features of interest. The Arnoldi method is applied to solve and track the partial

eigenvalues for the integrated system around a reference point with small negative real

part and frequencies of 0.1-0.7Hz. The targeted critical modes are dominantly

participated by the speed state variables in the majority of the synchronous generators in

the system. The focus is put on the damping ratio of the inter-area mode in this case. A

series of tests are performed as listed in Table 4.6, with the resulting damping ratios

calculated. Time domain simulations are also provided to support the eigenvalue

analysis with a self-clearing 60ms three-phase fault at bus 24.

A test comparing FF and FB type PQ controls in the VSC with different DC link

operating conditions has been carried out in this case. Both types of PQ controls result

in very similar inter-area mode damping with an increasing DC link power, which is

different from the case of the two-area system presented before. As the AC system

voltages are more stable due to the highly meshed nature of the representative GB

system, the FF type PQ controls act in a manner equivalent to very fast FB type PQ

controls. It is observed in Table 4.6 that the system moves from unstable (ξ =-0.42%) to

marginal stable (ξ =0.08%) with increasing DC link power from 100MW to 900MW

this time in both cases. Such results are validated in Fig. 4.16, which compares the

effect of FF and FB type controls as well as the effect of different DC link operating

points on the tie-line 8-10 power responses following the AC fault. It should be noted

that what would typically be considered a satisfactory damping (i.e. the resultant peak


- 127 -

power deviation to be reduced fewer than 15% of its value at the outset within 20s) has

not been achieved in this case.

Table 4.6 Inter-area mode damping ratio for case studies in GB system.

Test cases with control

settings in test case 1 DC link power Inter-area mode ξ %

FF and FB type controls

100MW -0.42%

500MW -0.15%

900MW 0.08%

Fast FBVac in VSC1 500MW 3.12%

Slow FBVac in VSC1 500MW -0.01%

Fast FBVac in VSC2 500MW -0.51%

Slow FBVac in VSC2 500MW -0.19%

500MW DC power

900MW DC power

1000

1100

1200

1300

1400

1500

0 5 10 15 20

Pow

er in

MW

Time(s)

FF type PQ FB type PQ

900

1100

1300

1500

1700

0 5 10 15 20

Pow

er in

MW

Time(s)

500MW DC power100MW DC powerFB type PQ

Fig. 4.16 Tie-line 8-10 power responses with FF/FB type VSC control.

As FBVac is found to have more impact on the inter-area oscillation than other VSC

controls, a better and satisfactory damping effect may be achieved. The tracked inter-

area mode damping ratios with FBVac in both VSCs of the DC link validate

aforementioned conclusion 3b before — A fast FBVac in the receiving area (VSC2)

reduces the damping of the inter-area mode while a faster FBVac in the sending area

(VSC1) improves the damping, as listed in Table 4.6. This is further shown in the time

domain simulations for the AC fault in Fig. 4.17. In both cases, the VSC controlled bus

voltage is improved with faster FBVac. However, only a faster FBVac in VSC1 increases


- 128 -

the system inter-area mode damping, and thus stabilizes the post fault system. The

opposite (though the effect is reasonably small) is seen when FBVac is employed in

VSC2. Care must be taken though when using FBVac with a very high bandwidth as it

may cause the connected AC system to become unstable in some circumstances.

0.98

1

1.02

1.04

0 5 10 15 20

V4

in p

.u.

Time(s)

1000

1100

1200

1300

1400

1500

0 5 10 15 20

Tie

line

pow

er in

MW

Time(s)

FBVac of 5Hz FBVac of 30Hz


0.98

0.99

1

1.01

1.02

0 5 10 15 20

V14

in p

.u.

Time(s)

1000

1100

1200

1300

1400

0 5 10 15 20

Tie

line

pow

er in

MW

Time(s)


FBVac of 5Hz FBVac of 30Hz

Fig. 4.17 (a) System responses with FBVac control in VSC1 and (b) System responses with FBVac control

in VSC2.

4.6. Effect of MTDC with Different Droop Controls

So far the effects of a point-to-point VSC HVDC link have been discussed in detail.

Further investigation of the assessment of VSC HVDC control strategies will consider

the case of a multi-terminal DC (MTDC) grid. The multi-terminal operation is

anticipated as a reliable solution for future grid interconnections such as the European

(a)

(b)


- 129 -

SuperGrid. Different control schemes adopted in a VSC MTDC system will change the

power injections into the connected AC grid and thus affect its dynamic performance.

Further analysis in this section compares the typical control strategies used in a four-

terminal DC system for windfarm and onshore connections based on the dynamic GB

system which is also a possible future scenario for the GB grid. A series of control

strategies are created for the MTDC grid, including the typical voltage margin control

and different droop control settings. The DC system power sharing and the

corresponding effects on the AC system are demonstrated.

MTDC Grid Control

A four-terminal DC grid is integrated to the dynamic GB model connecting one

windfarm and three onshore buses. The power flow directions at the original operating

point are also shown in Fig. 4.18.

27

26

2829 C

NN C

1 2

C

H

3

F

4

5

N 6

WF

7

8N

9 10

C11

N

15

F

12

13 14

C

16

C

1917

C

2022

21N

C

C

F

18

F

23

24

25

F C

H:Hydro F:FossilCoal N:Nuclear C:CCGT WF: Wind Farm

Bus

Double OHL

Load&Shunts

Reactor

Transformer

HVDC Lines

H

P1

P2

P3

GSVSC1

GSVSC2

GSVSC3

170km DC

cable

WFVSC

170km DC

cable

70km DC

cable

Fig. 4.18 Diagram for the integrated GB system and MTDC grid.

Three different types of control scenarios are designed for the GSVSCs and their Vdc-P

characteristics as illustrated in Fig. 4.19. Control scheme 1 adopts a two-stage voltage


- 130 -

margin control to allow the role of DC voltage regulation to be transferred to other

converters when the DC voltage regulating converter reaches its power limit (e.g. from

GSVSC3 to GSVSC2). Enhanced DC system reliability is achieved in comparison to

the conventional one-stage voltage margin control due to a reduced reliance on

communications. However, at each instant, there is still only one converter station

responsible for the DC voltage regulation.

Control scheme 2 is a standard Vdc-P droop control, which allows a certain amount of

variations in the DC voltage for each converter, and hence all converters share the

responsibility of voltage regulation. During operation, the converters’ power set-points

are adjusted by the measured DC voltages according to the droop lines. The slope of a

droop line indicates the degree of sensitivity of a converter’s output power to its DC

voltage variations.

Control scheme 3 is a combination of the concepts used in the previous two control

schemes where essentially a two-stage voltage droop control is presented. The dead-

band is introduced in GSVSC2 and GSVSC3 to allow them to operate in constant power

control mode for normal operation, so that their output power will be unaffected during

small system disturbances. However, they will still be able to return to voltage droop

control mode when the measured DC voltage exceeds the constant power operating

limits (V*low and V

*high).

The role of the windfarm side VSC is similar to a slack bus in the AC grid. It is there to

absorb all the power generated by the windfarm and also provide a reference frequency

for the wind turbines. To do so, the WFVSC is configured to maintain a constant

voltage at the PCC bus of the windfarm, and it also provides a constant frequency

reference. The initial operating point of the system is that GSVSC1 and the WFVSC are

injecting 1.4GW and 1.7GW power, respectively, into the DC grid. GSVCS2 and

GSVCS3 each receive 1.2GW and 1.9GW from the DC grid. Detailed controller

parameters are given in Table 4.7. The value Kslope = 15 is selected to provide an

appropriate trade-off between the steady-state DC voltage error, the response speed, the

dynamic performance and the MTDC stability [96]. Since the purpose is to compare the

performance of different MTDC control schemes, the same value is applied in all


- 131 -

control strategies. The DC lines are operating at ±320kV with lengths shown in Fig.

4.18.

Rectifier Inverter

GSVSC2

0

GSVSC1

0

GSVSC3

0

Rectifier Inverter

GSVSC1

0

GSVSC2

0

slope

dc

PK

V

GSVSC3

0

Rectifier Inverter

GSVSC1

0

GSVSC2

0

GSVSC3

0

Control Scheme 1: Voltage Margin Control

Control Scheme 2: Droop Control

Control Scheme 3: Droop Control with Dead-band

dead-band

Vdc Vdc Vdc

Vdc Vdc Vdc

Vdc Vdc Vdc

Vdc_low* Vdc_low

*

Vdc_high*

Vdc_high*

Vdc*

PmaxPmin

PrefPref

PmaxPmin PmaxPmin

Vdc*

Pref

PmaxPmin PmaxPmin PmaxPmin

PmaxPminPmaxPminPmaxPmin

Pref

Vhigh*

Vlow*

Vhigh*

Vlow*

Fig. 4.19 Vdc-P characteristics for the three control schemes.

Table 4.7 Data for MTDC control schemes (Fig. 4.19).

Control

Scheme

Grid Side Converters

GSVSC1 GSVSC2 GSVSC3

Voltage

Margin

Vdc_high* = 1.035p.u.

Vdc_low* = 0.96p.u.

Vdc_high* = 1.02p.u.

Vdc_low* = 0.97p.u.

Vdc* set from load

flow

Droop Kslope = 15 Kslope =15 Kslope =15

Droop with

dead-band

Vhigh* = 1.015p.u.

Vlow* = 0.97p.u.

Vhigh* = 1.015p.u.

Vlow* = 0.97p.u.

Kslope =15

* operating point Pref values are obtained from load flow results

Power Sharing in DC Grid

The power sharing in the DC grid can be affected by the droop gains. A brief

explanation is provided here. For DC network power flow, assuming a monopolar,


- 132 -

symmetrical grounded DC grid, the system can be described using the following

equations:

dc dc dcI = Y U (4.15)

dc dc dcP = 2U I (4.16)

2

dcdc dc

dc

PY U - = 0

U (4.17)

where Ydc is the DC network admittance matrix. When converters are under droop

control scheme, there is one more constraint they have to follow:

* *( )dci slopei dci dci dciP K V V P (4.18)

where superscript * stands for the reference point. The above equations (4.17) and (4.18)

can be solved iteratively with a Newton-Raphson method to calculate the voltages on all

DC buses. Thereafter, the power injections at the GSVSCs terminals are calculated.

Droop gain Kslopei can be adjusted until the power injection at the terminal meets the

requirement of the connected AC system if provided. By this means, the value of Kslopei

can be determined for droop control schemes. Values like the DC line impedances and

converter losses are normally invariable. Then the desired AC grid power injection

scenario is usually achieved by properly designing the droop gain settings.

Simulation Studies for Wind Power Injection

A sudden 500 MW rise of wind power injection to the DC grid is firstly simulated as an

event for this case study, investigating the AC side power injection affected by different

MTDC control schemes depicted in Fig. 4.19. This might, for example, represent the

extreme case of several strings in a windfarm being switched in. The responses of the

key parameters in both the DC and the AC sides of the system are presented under the

three MTDC control schemes.

DC System Responses

Fig. 4.21 (a) shows the output power from the three GSVSCs under different control

schemes, and the resulting power flow shows very different power sharing scenarios. In


- 133 -

order to demonstrate clearly how the GSVSCs react to the injected wind power, Fig.

4.20 is provided with indexes (1) to (3) indicating the sequence of the actions taken in

the converters. The total power change in each terminal during the process is also

illustrated.

WF

GSVSC1

GSVSC2

GSVSC3

∆P=500MW

DC

Grid

∆P=0MW

∆P=263MW

∆P=190MW(1)

(2)

WF

GSVSC1

GSVSC2

GSVSC3

∆P=500MW

DC

Grid

∆P=151MW

∆P=161MW

∆P=143MW(1)

(1)

WF

GSVSC1

GSVSC2

GSVSC3

∆P=500MW

DC

Grid

∆P=232MW

∆P=41MW

∆P=190MW(1)

(2)

(1)

Voltage margin control Droop control

Droop control with dead-band

(2)

(3)

Fig. 4.20 DC grid power change for different control schemes.

10.0 10.2 10.4 10.6 10.8 11.0

1200

1300

1400

1500

GS

VS

C2

In

jectio

n P

ow

er

(MW

)

Time (s)

10.0 10.2 10.4 10.6 10.8 11.0

1950

2000

2050

2100

GS

VS

C3

In

jectio

n P

ow

er

(MW

)

Time (s)10.0 10.2 10.4 10.6 10.8 11.0

-1500

-1400

-1300

-1200

GS

VS

C1

In

jectio

n P

ow

er

(MW

)

Time (s)


Droop Control

Droop Control with Deadband

-1172

-1253

-1403

-1404

1455

1353

1233

2103

2062

1192 1913

(a) power injections

(b) injection bus voltages

(c) DC voltages

10 12 14 16 18 20

1220

1230

1240

1250

1260

Po

we

r in

lin

e1

0-1

5 (

MW

)

Time (s)10.0 10.2 10.4

1.00

1.01

1.02

1.03

1.04

GS

VS

C1

DC

vo

lta

ge

(V

p.u

.)

Time (s)

10 12 14 16 18 200.9995

1.0000

1.0005

1.0010

1.0015

Bu

s1

0 V

olta

ge

(V

p.u

.)

Time (s)10 12 14 16 18 20

0.9995

1.0000

1.0005

1.0010

1.0015

1.0020

1.0025

Bu

s7

Vo

lta

ge

(V

p.u

.)

Time (s)10 12 14 16 18 20

0.999

1.000

1.001

1.002

1.003

Bu

s1

6 V

olt

ag

e (

V p

.u.)

T ime (s)

(d) tie-line powers

Fig. 4.21 Simulation results for 500 MW wind power injection.


- 134 -

For voltage margin control, the GSVSCs react to the wind power injection in the

following sequence: (1) the injected wind power is firstly transferred by GSVSC3

which is in constant DC voltage control. (2) The duty of DC voltage regulation is then

changed to GSVSC2 when GSVSC1 turns into constant power control mode after

reaching its maximum power limit. (3) Since GSVSC2 is capable of transferring the rest

of the injected wind power, GSVSC3 remains in constant power control mode and its

output power is unaffected after the event.

Standard droop control has the characteristic that all converter stations participate in DC

voltage control, and hence all GSVSCs in the DC grid react to share the injected wind

power. Therefore, the GSVSCs modify their power transfer simultaneously (Fig. 4.20)

to reach a new stable operating point. The amount of power shared by each converter is

affected by its own droop gain, as discussed in the previous section. This can be

properly designed in order to achieve a desired power injection scenario.

For control scheme 3, where a dead-band is introduced into the droop control, GSVSC1

and GSVSC2 were initially in constant power control mode. Similar to the voltage

margin control, the GSVSCs react to the wind power injection in the following

sequence: (1) GSVSC3 adopts the standard droop control, and it changes its operating

point to transfer the wind power until it reaches its maximum power limit. (2) After

GSVSC3 enters its constant power control mode, the other two GSVSCs turn into droop

control mode, and they start to modify their operating points and share the rest of the

injected wind power. The amount of power distributed to GSVSC1 and GSVSC2 again

is affected by their droop settings. Fig. 4.21 (c) gives the behaviours of the DC side

voltages. It is clear that, droop controls, which give an allowance for DC voltage

variations, end up with more smooth DC voltage transients in comparison with voltage

margin controls which force a constant DC voltage.

Effect on AC System

The resulting power flow scenarios in the DC lines lead to different AC system

behaviours. Fig. 4.21 (b) shows the resulting injection bus voltages. It is generally


- 135 -

observed that the magnitude of the transient overshoot is proportional to the amount of

power change (∆P) in the bus (e.g. for injection bus 7, a larger voltage transient is seen

when it has a larger ∆P). The magnitude of the oscillations is small here due to the small

capacity of the MTDC grid in comparison with the whole AC system. However, this

can grow larger when more power is transferred from the DC links into the grid.

The tie-line 10-15 power responses (Fig. 4.21 (d)) are most affected when the power

injections of GSVSC2 and GSVSC3 change. However, in contrast to the DC voltage

responses, the power injection scenario provided by voltage margin control leads to a

smaller power oscillation in the tie-line. This is mainly due to the fact that the total

amount of power change in the whole DC grid is the smallest under the voltage margin

control (Fig. 4.20).

Simulation Studies for AC System Fault

This case study investigates the integrated system behaviour for AC side events under

different MTDC control schemes. A 100ms self-clearing three-phase fault is created at

bus 10 and again the focus is on the responses in both the AC and the DC side of the

system as presented in Fig. 4.22.

It is seen from Fig. 4.22 (a) that the power injections at the three GSVSCs are disturbed

when the AC system fault occurs. The worst case scenario is seen when voltage margin

control is adopted in the MTDC grid. GSVSC3 is operating at its maximum power

capability which is then reduced during the AC system fault event due to a drop in the

converter AC side voltage. The PLL in GSVSC3 also becomes inaccurate during the

fault. Therefore, the controls in GSVSC3 become saturated for a short period of time

when voltage margin control is adopted. This causes the “spike” in the resulting

GSVSC3 power response. In order to keep a constant DC voltage, the voltage margin

control scheme results in larger power oscillations in comparison with the other two

control schemes.

The ability of smooth DC voltage control for a droop control scheme is again shown in

Fig. 4.22 (c). A better DC voltage response is given when all GSVSCs are in standard

droop control mode. The other two control schemes result in larger overshoot in the DC


- 136 -

voltages. However, the AC side injection bus voltages, which should be affected by the

DC voltage variations, turn out to be very similar. This is because the differences in the

DC side responses are too small (fast) to be noticed by the AC side and the generators

connected at the injection buses are also contributing in voltage regulation. Therefore,

the injection bus voltages are not significantly affected by the control schemes adopted

in the MTDC grid under AC faults. As a result, the injection bus voltage responses

coincide as shown in Fig. 4.22 (b), and the tie-line power flow is also not affected (Fig.

4.22 (d)) for the same reason.

The best MTDC control strategy thus varies depending on the specific structure of the

connected AC system, as well as the requirement on the power injection at each

terminal, and the transient and static performance of the DC system. This requires a full

mathematical model of the integrated system to optimize the power flow based on the

provided requirements from the AC grid.

10.0 10.2 10.4 10.6 10.8 11.00.4

0.6

0.8

1.0

Bu

s 7

Vo

lta

ge

(V

p.u

.)

Time (s)10.0 10.2 10.4 10.6 10.8 11.0

0.0

0.5

1.0

Bu

s 1

0 V

olta

ge

(V

p.u

.)

Time (s) 10.0 10.2 10.4 10.6 10.8 11.00.8

0.9

1.0

1.1

Bu

s 1

6 V

olta

ge

(V

p.u

.)

Time (s)

10.0 10.2 10.4

-1500

-1000

-500

0

500

GS

VS

C1

In

jectio

n P

ow

er

(MW

)

Time (s)10.0 10.2 10.4

0

500

1000

1500

GS

VS

C2

In

jectio

n P

ow

er

(MW

)

Time (s)10.0 10.2 10.4 10.6 10.8 11.0 11.2 11.4

1500

2000

GS

VS

C3

In

jectio

n P

ow

er

(MW

)

Time (s)

9.9 10.0 10.1 10.2 10.3 10.4 10.50.95

1.00

1.05

1.10

GS

VS

C1

DC

vo

lta

ge

(V

p.u

.)

Time (s)10 11

0

1000

2000

3000

Po

we

r in

lin

e1

0-1

5 (

MW

)

Time (s)

(a) power injections

(b) injection bus voltages

(c) DC voltages (d) tie-line powers


Droop Control

Droop Control with Deadband

Fig. 4.22 Simulation results for AC system fault.


- 137 -

4.7. Conclusion

This chapter provides a systematic comparison of the effects of VSC HVDC controls on

the dynamic behaviour of an AC/DC system. Investigations have been carried out on

typical outer voltage and power control schemes for a single converter, as well as the

MTDC control strategies for multiple converters. The effect of VSC outer controller

parameter settings are analysed via modal analysis techniques, and are validated through

transient simulations. It has been particularly shown that the VSC outer loop control

settings can have a significant impact on AC system inter-area oscillation damping.

Therefore, well-tuned outer controllers might be able to damp the system oscillations

appropriately such removing the need for additional supplementary POD controllers

completely, in particular if these are local POD controllers, or to inform the design of

additional wide area monitoring based POD if these are to be installed. Typical

conclusions obtained from the results are illustrative for a very standard two-area

system and a system based on reality, and they are therefore helpful for providing

insights and understanding the possible influences brought by DC controls on the AC

dynamics. For VSC outer controls in a parallel VSC HVDC link, typical conclusions

can be summarized as:

i. The operating point of the DC link (power flow) and the AC voltage control in

VSCs have larger influences on the AC system inter-area oscillation than other

VSC controls. For an embedded VSC HVDC link (in parallel with AC tie-lines), if

FF type PQ controls are used, it normally increases the damping of the inter-area

mode at higher power flow. However, when FB type PQ controls are used, their

effects on the damping of inter-area mode may depend on the system structure.

ii. Additionally, FBVac in the receiving area of an embedded VSC HVDC link with

higher bandwidth reduces the damping of the inter-area mode, while one in the

sending area (VSC1) improves the damping. Varying the bandwidth of FBVac has

less influence on the damping ratio of the inter-area mode at higher DC link

power. However, the FBVac bandwidth variation has larger influence on the

frequency of the inter-area mode at higher DC link power.


- 138 -

For different MTDC control strategies employed in a four-terminal DC system, the key

identifications can be summarized as:

i. From the perspective of DC grid power change event, the adopted MTDC control

scheme can significantly affect the DC power flow and thus leads to different

corresponding AC system responses. The power injected at each terminal of a

MTDC grid can be estimated by the DC grid load flow, taking into consideration

the influences of the adopted MTDC control scheme in order to achieve an optimal

power injection for the connected AC grid.

ii. In terms of AC system fault events, the effect of MTDC control scheme is mainly

reflected in the transient behaviours of the DC side system. The AC system

voltages and tie-line power flows are not significantly affected when different,

reasonably tuned MTDC control schemes are adopted in this case.

Chapter 5. Potential Interactions between VSC HVDC and STATCOM

- 139 -


Chapter 5. Potential Interactions between

VSC HVDC and STATCOM

This chapter analyses the dynamic behaviour of a power system with both FACTS

and VSC HVDC, in particular, possible potential interactions between a STATCOM

and a VSC in a point-to-point HVDC link. The investigation considers different

system conditions regarding factors of electrical distances between the devices, the

AC system strength, as well as possible control schemes that are typically employed

in these devices. A generic linearized mathematic model of a reduced system is

firstly developed, where a combined method involving relative gain array (RGA)

and modal analysis is applied to identify the interactions within the plant model and

the outer controllers. Potential adverse interactions are highlighted with weak AC

system conditions. The identifications are further tested by creating a set of

scenarios integrating both the STATCOM and VSC HVDC into the dynamic GB

system. Results show a collaborative operation between the STATCOM and the

closely located VSC with reasonably tuned controllers in a strong AC system.

5.1. Interactions in HVDC and FACTS

The Electricity Ten Year Statement shows an increased number of DC transmission

interconnections being proposed for connecting windfarms sited far offshore and for

reinforcement of the onshore network via undersea DC cable links. Meanwhile, as

the amount of windfarm installations increases, FACTS devices like STATCOMs

will be used to help wind power generation to achieve grid code compliance [97].

STATCOMs also have a potential synergy with LCC based HVDC links for reactive


- 140 -

power supply [20]. A natural consequence of increasing quantities of actively fast

controlled devices is that these components might be located in the electrical

proximity to each other, especially for a VSC based multi-terminal HVDC (MTDC)

grid in the future. It is therefore important to understand their control interactions.

This chapter considers the particular case of a STACOM, installed perhaps as part of

a windfarm and located close to a VSC-based HVDC link.

Valuable work regarding interaction studies has been carried out in many aspects.

Studies regarding concurrent operation of multiple FACTS devices or FACTS

devices and conventional LCC HVDC links indicate that there exist potential

interactions [98-101]. Many methods have been proposed and applied in order to

study these interactions. The concept of induced torque is introduced in [100] to

study the interactions between power system stabilizers and FACTS stabilizers, and

their controller tuning effect on the overall system is analysed in [102]. Furthermore,

the RGA [103] method has been shown in [99, 104] to be suited to quantify the

interactions in power system steady-state and dynamic studies. It was also suggested

in [98] that modal analysis can be used to highlight how modifications in one

FACTS controller can affect another. Several factors, including the electrical

distances between the devices and the AC system short circuit ratio, have been

identified as influencing the degree of interaction.

However, the interactions between VSC HVDC links, which use substantially

different control to LCC HVDC, and FACTS devices have not yet been thoroughly

investigated. The cascaded control structure in a VSC HVDC means that interaction

with a STATCOM can occur through multiple control structures and cannot

completely be identified through a single conventional method.

It is therefore reasonable to propose a combined method that utilizes RGA to

quantify the plant model interactions and modal analysis to illustrate the outer

controller interactions. Different types of VSC control strategies are also considered

since this may affect the degree of controller interactions. The study is initially

carried out in a small test system to facilitate physical understanding of interactions.


- 141 -

Following this, a set of scenarios is then created using the dynamic equivalent model

of GB system to validate findings.

5.2. STATCOM Model for Stability Studies

A STATCOM is a fast acting power electronic device based on VSCs, which can act

as either a source or a sink of reactive power to an electricity network. It is a shunt

device of the FACTS family to regulate voltage at its terminal by controlling

reactive power flow. It is normally installed to support electricity networks that have

a poor power factor and often poor voltage regulation, achieving power system

dynamic compliance between lead/lag 0.95 power factor. By keeping a high power

factor in the system, the transmitting current can be reduced for less energy loss in

the transmission system. The voltage source is created from a DC capacitor, and

thus a STATCOM has very little inherent active power capability. However, this can

be enhanced by connecting suitable energy storage devices (e.g. batteries, pumped

storage, etc.) to the DC capacitor. A typical structure is illustrated in Fig. 5.1,

showing also the coupling transformer and reactor.

C

R+jX or

G+jB

Tc

AC system

Bus

E V

i

Vdc

V

V*

0

PM0

PM

Vdc

Vdc*

kp+ki/s

kp+ki/s

V

Kslope

Vref

Imin Imax Inject QAbsorb Q

VDC_min I

(a) (b)

Fig. 5.1 STATCOM model (a) with δ-PM control (b) V-I characteristic.

The typical phase angle (𝛿) and the modulation index (PM) [50] control structure for

STATCOM is also presented. Please see Chapter 2 for detailed description of this

control (i.e. power angle control). For power system voltage and angle stability


- 142 -

studies, the STATCOM model can be expressed by power balance and voltage

conversion equations. After linearization, the equations are:

dc dc dc

dc

T

dc

dc

dc

VV G VV ( G cos( δ δ ) B sin( δ δ )

V A V B V VCV

δ

GV V G cos( δ δ ) V B sin( δ δ )

CVV

VG cos( δ δ ) VB sin( δ δ )V

CVδ

VV G sin( δ δ ) VV B cos( δ δ )

CV

2

0 0 00 2

0 0 0 0

0 00

0 0 0 0

2

(5.1)

dc MV V P 3

8 (5.2)

where the parameters are as specified in Fig. 5.1. The controller limits are defined

based on the controller current limits (e.g. IGBT current limits), and the effect of

transient performance needs to be factored into the controller tuning. However, the

limits of the phase angle and the modulation index do not necessarily limit the actual

current. According to the V-I characteristic, the modulation index limits PM_max and

PM _min can be calculated as:

ref slope maxM _ max

dc _ ref

ref slope minM _ min

dc _ ref

V K IP

V

V K IP

V

2 2

3

2 2

3

(5.3)

The phase shift limits δmax and δmin need to be derived by calculating the steady-state

equation for the control system at Imax and Imin [50].

5.3. Generic Interaction Study

The VSC HVDC model described in Chapter 2 is used here with the developed

STATCOM model. In order to quantify the interactions between a STATCOM and a

VSC in the HVDC link, a reduced test system was established with only a VSC


- 143 -

HVDC link and a STATCOM interconnected through a line with adjustable

impedance (Fig. 5.2). This removes unnecessary detail that could clutter and obscure

results. A voltage source behind impedance is used to represent an AC network. The

system strength can be parameterized by varying the value of the impedance, and

thus the short circuit ratio (SCR). The VSC controls its injection current to the

system; while in turn, the system provides the reference bus voltage (bus 2) to the

phase locked loop (PLL) and the VSC. The STATCOM communicates with the AC

system through voltage exchange.

The intention behind using a reduced system model is to obtain general interactions

before applying the models to a large and specific test system. Our method is to use

RGA to analyse the interactions in the plant model, as the method does not depend

on the controllers. Outer controller interactions can be investigated through modal

analysis techniques.

Xvsc

i σ

v θ2

Xstatcom

VSC HVDC Link

E δv δ3 0

C

e θ

5

refv 0

Xs

Line

1 2

3

4

STATCOM

P

Vdc2

Ceq

VSC1 VSC2

External

Grid Vdc1

Ceq

Fig. 5.2 Reduced system model for generic interaction study.

RGA for Plant Model

Since firstly proposed by Bristol [103], RGA provides a measure of interactions and

is normally used as a tool for multi-input multi-output (MIMO) system optimal

input-output pairing. However, here it is possible to consider it as a way to quantify

the degree of interaction between the plant model of the STATCOM and VSC.


- 144 -

One way to calculate the RGA of a MIMO system is to use the steady-state gain

matrix obtained from system model equations. Let uj and yi denote an input-output

pair of a plant G(s), the relative gain can be expressed as the ratio of two extreme

cases [45]:

,

,

ˆ

0

0

1u k jk

y k ik

all other loops open

i

jij

ij all other loops closed ij jiij

i

j

y

u gλ G G

gy

u

(5.4)

The RGA element ij measures the influence of all other variables on the gain

between input uj and output yi. If ij=1, all the other control loops have no impact on

the control pair uj and yi, and this is the case where no interaction exists. Thus ij≠1

indicates there are interactions between the other control loops and the selected

control pair. The closer the value of ij is to the unity, the smaller the interaction is.

These important properties of RGA (summarized in [45, 104]) are used for

evaluating the degree of interaction in this case.

To study the interactions within the plant models, the outer control loops of the

STATCOM and the VSC should be removed. The resulting plant model is within the

dashed square shown in Fig. 5.3 where the plant manipulated inputs and outputs are

labelled. Inputs id* and iq

* are the reference dq current values in VSC2 while PM and

δ are the manipulated inputs for the STATCOM. The outputs are the calculated

results from the network which are fed back to the STATCOM and VSC2.

By linearizing the system model at an operating point, the system steady-state gain

matrix can be calculated for the defined inputs and outputs. As there are four inputs

and outputs, the plant model G(s) will be a 4×4 matrix with each element

representing a transfer function between a corresponding input and output pair (e.g.

g21 stands for the transfer function between input 1 and output 2). According to the

definition in equation (5.4), the RGA of the four inputs and four outputs system can

be derived based on equation (5.5).


- 145 -

dq

current

control

VSC

net

work

STATCOM

edq

Plant G(s)u1

u2

id*

iq*

u3

u4

PM

idq

y1P

y2v2

E δ v3

y3

y4

Vdc2

outer

control

Modulation

& phase

control

Fig. 5.3 RGA plant model with selected inputs and outputs.

* *

d q a

* *T d q a

dc dc dc dc

* *

d q a

* *

d q a

P P P P

i i δ m

v v v v

i i δ mλ ...RGA G G , G

... λ V V V V

i i δ m

v v v v

i i δ m

2 2 2 2

11 1

44 2 2 2 2

3 3 3 3

(5.5)

When calculating the RGA from the steady-state gain matrix (frequency ‘0’), the

resulting RGA for two different lengths of the interconnecting line is given in Table

5.1. The diagonal elements in bold show the corresponding control pairs where the

input has dominant effect on the output. The RGA element value of ‘1’ for the

control pairs of u1-y1 and u3-y3 shows that these two control pairs are not affected by

any other control loops in the system. Interactions are mainly detected between the

VSC q-axis current control loop iq*-v2 and the STATCOM modulation index control

loop PM-v3. RGA values larger than 1 indicate that the control pairs are dominant in

the system, but the other loops are still affecting the control pairs in the opposite

direction. The higher the value, the more correctional effects the other control loops

have on the pair. This interaction becomes more significant as the electrical distance

between the VSC and the STATCOM decreases (RGA number 1.42 to 1.96).

The RGA analysis suggests interactions between VSC2 iq*-v2 and STATCOM PM-v3

in the plant models without outer control loops. However, in normal operation, outer


- 146 -

control loops for the two components need to be considered. To further show how

VSC and STATCOM affect each other through outer controls, a parametric analysis

based on the modal analysis and transient simulations was performed.

Table 5.1 RGA results for selected inputs and outputs.

Input

Output

Line: (1+20j) Line: (0.5+10j)

id* iq* δ PM id* iq* δ PM

y1:P 1 0 0 0 1 0 0 0

y2:v2 0 1.42 0 -0.42 0 1.96 0 -0.96

y3:Vdc 0 0 1 0 0 0 1 0

y4:v3 0 -0.42 0 1.42 0 -0.96 0 1.96

Outer Control Interactions

The reduced system model is also used for analysing the outer control interactions.

To do this, VSC2 is configured with typical outer controls of: (1) the Feedback P

and Q control and (2) the Feedback P and Vac control, as described in Chapter 2.

For convenience, these controls will be referred to as PQ control and P-Vac control

in the following text of this chapter. The other types of VSC control, such as DC

voltage control or droop type control, are focusing more on the control of the DC

side components rather than the AC system parameters, and they are not likely to

have interactions with the STATCOM. This outer control interaction study considers

the variations of system conditions in the short circuit capacity of the AC grid and

the controller parameters in the electronic devices.

VSC2 with PQ Control

Firstly, VSC2 is configured to PQ control mode. Based on the results obtained from

the RGA analysis of the plant models, significant interactions between VSC HVDC

and STATCOM occur when they are closely located. Therefore, in this case, low

transmission impedance (e.g. R=0.266Ω and X=2.645Ω) is considered. The focus

will then be put on the strength of the AC system which is defined by the SCR as:

2

converter MW rating converter MW rating

ac thV ZSC MVA

SCRDC DC


- 147 -

As stated in [20], the AC system strength is classified as (1) high (SCR>5), (2)

moderate (3<SCR<5) and (3) low (SCR<3), as the source impedance Xs in Fig. 5.2

varies. For this study, a weak AC system with SCR=1.5 and a strong AC system

with SCR=10 are assumed to represent two extreme system strength conditions.

The method utilizes a parametric analysis regarding different system and controller

configurations. Modal analysis was used in support of the time domain simulations

to show how those critical modes are affected under different controller settings. The

proportional and integral gains of the STATCOM PM control (Fig. 5.1) are

configured to be kp and ki=ckp (c=5). This form makes the variations in the

STATCOM controller parameters easier for the case studies.

Modal analysis is firstly applied to the reduced system model with both a weak and

a strong AC network. For each system configuration, the gain in the STATCOM PM

control is increased from 0.1 to 1 with a step of 0.1. All the system modes are

monitored each time during the process, and those that are affected by the gain

change are recorded. However, since some system modes are influenced by more

than one state variable in the model, it is necessary to see the contribution of each

state variable for a particular mode that is affected during the process of the

controller’s gain change. This is achieved by calculating the participation factors of

the system state variables for these modes. The relative participation of the states in

a mode can be weighed, and thus the interactions of the state variables are shown.

The trajectories of system eigenvalues for the parametric analysis are plotted in Fig.

5.4 and Fig. 5.5 for strong and weak AC systems respectively. The modes that are

significantly affected (modes with obvious movement trajectory) are highlighted

with labels in the two figures. The participation factors of the key system state

variables related to the labelled modes are also given in Table 5.2 and Table 5.3, for

strong and weak AC systems respectively. In this case, only selected state variables

with significant contributions (participation factor >0.1) in at least one of the critical

modes are listed.

For a strong AC system, as shown in Fig. 5.4 and Table 5.2, the controller gain (kp)

increase in the STATCOM only has a small effect on one system mode (Mode 1) on


- 148 -

the negative real axis1, and it is dominantly participated by the STATCOM PM

control state variable. A strong AC system provides a firm AC voltage which

weakens the degree of interaction between the STATCOM and VSC HVDC.

However, in the case of a weak AC system, the network voltage is mainly controlled

by the STATCOM. Variations in the STATCOM PM control parameters can

therefore affect a number of system modes as shown in Fig. 5.5. It is seen that the

increase of kp in the STATCOM does not only affect its own mode (Mode 5 which is

dominantly participated by STATCOM PM control state), but also four other modes

which involves state variables of the outer controllers in the VSC HVDC link and

the PLL, as presented in Table 5.3.

-1000 -900 -800 -700 -600 -500 -400 -300 -200 -100 0-2000

-1000

0

1000

2000

Real

Imag

System eigenvalues

-20 -15 -10 -5 0

-40

-30

-20

-10

0

10

20

30

40

Real

Imag

Low frequency eigenvalues

Mode1Low frequency

eigenvalues

Fig. 5.4 Root loci of system eigenvalues with STATCOM voltage controller gain varied from 0.1 to 1

with a strong AC network.

Table 5.2 State variables participation factor for the affected modes.

Key State Variables Participation Factor (Normalized)

Mode 1

STACOM PM controller state 0.99 *other state variables with participation factor less than 0.1 are NOT listed

-800 -700 -600 -500 -400 -300 -200 -100 0-2000

-1000

0

1000

2000

-20 -15 -10 -5 0

-40

-30

-20

-10

0

10

20

30

40

Real

Imag

Mode1 Mode2 Mode3Mode4 Mode5

System eigenvalues Low frequency eigenvalues

Real

Imag

Low frequency

eigenvalues

Fig. 5.5 Root loci of system eigenvalues with STATCOM voltage controller gain varied from 0.1 to 1

with a weak AC network.

1 A mode on the negative real axis corresponds to a non-oscillatory mode that decays — the larger its

negative magnitude, the faster the decay.


- 149 -

Table 5.3 State variables participation factor for the affected modes.

Key State Variables Participation Factor (Normalized)

Mode 1 Mode 2 Mode 3 Mode 4 Mode 5

VSC2 P controller state 0.29 0.10 0.36 0.37 0.035

VSC2 Q controller state 0.18 0.25 0.024 0.042 0

VSC2 PLL controller state 1 0.13 0.043 0 0 0

VSC2 PLL controller state 2 0.018 0.16 0 0 0

STACOM δ controller state 0.37 0.44 0.59 0.18 0.096

STACOM PM controller state 0.012 0 0 0 0.87

VSC1 Vdc controller state 0 0 0 0.36 0 *other state variables with participation factor less than 0.1 are NOT listed

Time domain simulations were also performed to validate the results obtained from

the eigenvalue analysis. Comparisons between the system responses for both weak

and strong AC system strengths when subjected to a three-phase AC short circuit

fault at bus 5 for 100ms are given in Fig. 5.6, where the STATCOM PM control gain

adopts kp=0.5 and kp=2.5.

0.9 1 1.1 1.2 1.3 1.4 1.5 1.60.8

1

1.2

ST

AT

CO

M V

ac p

.u.

0.9 1 1.1 1.2 1.3 1.4 1.5 1.6-20

0

20

VS

C2 Q

MV

Ar

0.9 1 1.1 1.2 1.3 1.4 1.5 1.635

40

45

50

VS

C2 P

LL d

eg

0.9 1 1.1 1.2 1.3 1.4 1.5 1.6160

180

200

220

VS

C2 P

MW

time(s)

0.9 1 1.1 1.2 1.3 1.4 1.5 1.60.6

0.8

1

ST

AT

CO

M V

ac p

.u.

0.9 1 1.1 1.2 1.3 1.4 1.5 1.6-200

0

200

400

VS

C2 Q

MV

Ar

0.9 1 1.1 1.2 1.3 1.4 1.5 1.6-100

-50

0

50

VS

C2 P

LL d

eg

0.9 1 1.1 1.2 1.3 1.4 1.5 1.60

100

200

300

VS

C2 P

MW

time(s)

Strong AC System SCR=10 Weak AC System SCR=1.5

STATCOM kp=0.5

STATCOM kp=2.5

STATCOM kp=0.5

STATCOM kp=2.5

Fig. 5.6 Comparison of system dynamic responses with a strong (left) and a weak (right) AC system.


- 150 -

According to the simulation results, the controller parameter change in the

STATCOM only affects its own output voltage with a strong AC system. The power

and PLL responses in the VSC2 are not affected as expected from the previous

modal analysis. However, when the AC system is weak, kp change in the

STATCOM affects the network voltage and thus the dynamic behaviour of VSC2

and the PLL, as shown by the figures in the right column of Fig. 5.6. The results in

this case suggest that the interaction between the STATCOM and VSC2 is more

significant when the connected AC system is weak. In other words, the controls in

the two components can more easily affect each other when they are not decoupled

by a strong AC system. However, even in the case of a strong interaction, variations

in the STATCOM voltage control do not worsen significantly the dynamic

performance of VSC2 PQ control nor that of the PLL in this case.

It is claimed in [105] that PLL has difficulties in reference angle tracking when the

connected AC system is weak. This can affect the performance of the outer PQ

controls in VSC2 and potentially the STATCOM which interacts strongly with the

VSC in such a system condition. Therefore, further tests consider the effect of a

parameter change in the VSC HVDC. This is demonstrated by increasing the

bandwidths of the PQ control loops in VSC2 (see Chapter 4 for details on bandwidth

variations) for weak AC system connection. The comparison is presented in Fig. 5.7

with the same 100ms AC fault at bus 5 each time.

According to the comparison given in Fig. 5.7, it can be observed that the

STATCOM PM control dynamic performance is improved when the bandwidth of

the P control in VSC2 is increased (from 5-15Hz). However, further increase of the

bandwidth of the VSC P control leads to adverse interactions between the

STATCOM and VSC2. The same bandwidth variation test is also performed for

VSC2 Q control. The results show that the VSC reactive power controller only

affects the dynamic behaviour of its output reactive power, but not the controllers in

the STATCOM, and thus they are not presented here.

The reason for the adverse interaction is analysed. This is mainly due to the fact that

the real power in the network is controlled by VSC2 and its dynamic responses vary


- 151 -

during the AC fault. When VSC2 P control loop bandwidth is increased, its real

power output response after the AC fault becomes steeper and with larger

overshoots. This real power flow will charge/discharge the DC capacitor of the

STATCOM causing STATCOM DC voltage oscillations. Meanwhile, as the AC

system is weak, the AC voltage is mainly controlled by the STATCOM. Therefore,

oscillations in the STATCOM DC voltage reflect in its AC side, thus affecting the

system AC voltage. The performance of the PLL and VSC2 Q control, which is very

sensitive to the system voltage variations, is then deteriorated. As illustrated in Fig.

5.7, increased oscillation magnitude is observed when the bandwidth of VSC2 P

control is changed from 15Hz to 30Hz. On the other hand, as the variations in the

VSC2 Q control loop bandwidth do not affect the AC voltage control in the

STATCOM, no adverse interactions occur.

VSC2 P Control 5Hz VSC2 P Control 15Hz VSC2 P Control 30Hz

1 1.1 1.2 1.3 1.4 1.5 1.6

0.9

1

1.1

ST

AT

CO

M V

ac p

.u.

1 1.1 1.2 1.3 1.4 1.5 1.6

-50

0

50

VS

C2 Q

MV

Ar

1 1.1 1.2 1.3 1.4 1.5 1.630

40

50

60

VS

C2 P

LL d

eg

1 1.1 1.2 1.3 1.4 1.5 1.6

180

200

220

VS

C2 P

MW

time(s)

Fig. 5.7 System responses with different VSC2 PQ control settings and a weak AC system.


- 152 -

Such phenomenon can be proved by comparing the DC voltage responses of the

STATCOM during the AC fault event, as presented in Fig. 5.8. With the bandwidth

of the VSC2 P control loop increases, the STATCOM DC voltage oscillates with

larger magnitude indicating the adverse interaction between the two devices caused

under such circumstances.

1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4

0.95

1

1.05

1.1

1.15

Vdc

p.u

.

time(s)

VSC2 P Control 5Hz

VSC2 P Control 15Hz

VSC2 P Control 30Hz

Fig. 5.8 STATCOM DC side voltage responses with different VSC2 P control settings.

VSC2 with P-Vac Control

The above adverse interactions can be mitigated by configuring the VSC in voltage

control mode. This section continues the above analysis but now VSC2 is applied

with P-Vac control. In this configuration, the reduced network AC voltage is jointly

controlled by both the STATCOM and VSC2. With an increased VSC2 P control

loop bandwidth, the same system AC fault event is applied and the resulting

responses are provided in Fig. 5.9.

With properly tuned voltage controllers (i.e. voltage control loop with reasonable

step responses), both the STATCOM and VSC2 contribute to the AC system voltage

compensation by supplying reactive power in a collaborative way during a fault

event in the system. Adverse interactions when PQ control is employed in VSC2 do

not occur in this case, as the system voltage is not worsened by the high bandwidth

P control loop. However, it should be noted that as both devices are controlling the

system voltage and are closely located, their voltage references need to be properly

parameterized depending on the required local power flow.


- 153 -

1 1.1 1.2 1.3 1.4 1.5 1.6

0.9

0.95

1

1.05

ST

AT

CO

M V

ac p

.u.

1 1.1 1.2 1.3 1.4 1.5 1.6

0

50

100

VS

C2

Q M

VA

r

1 1.1 1.2 1.3 1.4 1.5 1.640

42

44

46

VS

C2

PL

L d

eg

1 1.1 1.2 1.3 1.4 1.5 1.6

180

200

220

VS

C2

P M

W

time(s)

VSC2 P Control 5Hz VSC2 P Control 15Hz VSC2 P Control 30Hz

Fig. 5.9 System responses with different VSC2 P-Vac control settings and a weak AC system.

5.4. Test on Dynamic GB System

To verify the interactions identified in the reduced model, the STATCOM and VSC

models are applied to the dynamic GB system developed in Chapter 3. A set of

scenarios regarding different electrical distances and control strategies was created

for testing. However, the SCR in such a multi-machine system with no extremely

weak transmission lines is usually high, and thus the interaction between the

STATCOM and VSC HVDC is expected to be small.

A VSC HVDC line is integrated to the AC system connecting bus 2 and bus 10,

carrying 500MW power flow. VSC1 is configured to regulate the DC voltage and

the switchable PQ control and P-Vac control are adopted by VSC2. A 225 MVA

STATCOM is also added to the system at the locations illustrated in Fig. 5.10. The


- 154 -

investigation is carried out by considering different STATCOM locations and VSC

HVDC control strategies.

27

26

2829 C

NN C

1 2

C

H

3

F

4

5

N 6

WF

7

8N

9 10

C11

N

15

F

12

13 14

C

16

C

1917

C

2022

21N

C

C

F

18

F

23

24

25

F C

H

VSC1

VS

C2

DC

ca

ble

Phase

Reactor

Hydro

OHL

Bus

Transformer

Load

& Shunt

H

C

N

F

WF

CCGT

Nuclear

Fossil

Wind

Farm

North

STATCOM

Location 1STATCOM

Location 2

STATCOM

Location 3

Fig. 5.10 Dynamic GB system with VSC HVDC link and FACTS.

Case Study 1 -Different STATCOM Locations

The selected locations are likely to have wind power injections or LCC HVDC

terminals where a STATCOM might be installed. The STATCOM attempts to

maintain a constant voltage of 1 p.u. at its connected bus. The converter at the

receiving end of the DC link (VSC2) is in PQ control mode that delivers a constant

500 MW active power from bus 2 to bus 10, while keeping the reactive power to

zero. The STATCOM is connected sequentially to three buses (10, 12, and 26). For

the first location, the STATCOM is closely coupled with the receiving end VSC, as

they are both trying to control either the voltage or the power of bus 10. The second

and the third locations are considered as loosely coupled conditions for the VSCs

and the STATCOM. A 100ms three-phase short circuit fault is applied at bus 1 in

the AC grid, and the system responses are monitored for different STATCOM

locations. The comparison of the responses is presented in Fig. 5.11.


- 155 -

In Fig. 5.11 (a), the voltage variations at bus 10 are significantly better damped

when the STATCOM is connected to the bus 10. When the STATCOM is placed at

the other two loosely coupled locations, its effect on the bus 10 voltage becomes

much smaller. As shown in Fig. 5.11 (b) and (c), the VSC controlled real and

reactive power responses are only affected by the STATCOM when it is closely

coupled to VSC2 (bus 10) as expected. With the STATCOM at bus 10 the

oscillations in the VSC controlled real and reactive power become smaller. This is

due to the better voltage profile at bus 10 during the fault when the STATCOM is

placed. This test verifies that the STATCOM has the largest effect on the VSC

HVDC connected bus voltage when it is placed at the location nearest to the VSC

HVDC link.

Case Study 2 - Outer Control Loop Interactions

The STATCOM is kept at bus 10 in this case. The two typical VSC HVDC outer

control schemes analysed before are tested in this case. Specifically, VSC2 outer

control loops are configured to be in PQ control and P-Vac control. Bus 10 is the

PCC (point of common coupling) bus for the VSC HVDC link. The 100ms three-

phase short circuit at bus 1 is again applied, and the integrated system responses are

recorded and presented in Fig. 5.12. The case with no HVDC is also included in the

results for comparison purposes.

The STATCOM is to maintain a constant voltage level at the PCC bus during the

fault. This voltage control is affected when the 500 MW VSC HVDC link is added.

The voltage oscillation at bus 10 is improved by adding VSC HVDC, and it is

further damped when P-Vac control is adopted in the VSC HVDC link, as shown in

Fig. 5.12 (a). This is expected as both STATCOM and VSC2 are contributing in

voltage control as shown in Fig. 5.12 (b) and (c). Here they act in a collaborative

way, as the voltage set points for the STATCOM and VSC2 are the same, which

agrees with the results shown in the investigation of the reduced network. Adverse

interactions when PQ control is employed in VSC2 do not occur as the connected

AC system is strong. However, with a short electrical distance between the

STATCOM and the VSC in voltage control mode, control interaction may occur


- 156 -

between the STATCOM and VSC2 as they are both trying to control the bus voltage.

The voltage reference set points for both devices need to be controlled in

coordination, otherwise adverse interactions might occur.

0 5 10 15 200.996

0.998

1

1.002

1.004

Bus 10 Voltage

time(s)

V p

u

0 5 10 15 2042.2

42.4

42.6

VSC2 Q

time(s)

Q M

VA

r

0 5 10 15 20500.3

500.4

500.5

500.6

500.7VSC2 P

time(s)

P M

W

STATCOM at bus 10

STATCOM at bus 12

STATCOM at bus 26

(a) (b)

(c)

Fig. 5.11 System fault responses for different STATCOM locations.

0 5 10 15 200.996

0.998

1

1.002

1.004

Bus 10 Voltage

time(s)

V p

u

STATCOM only

STATCOM and VSC2(PQ control)

STATCOM and VSC2(PVac control)

0 5 10 15 20

-50

0

50

100

STATCOM Q

time(s)

Q M

VA

r

0 5 10 15 200

50

100

150VSC2 Q

time(s)

Q M

VA

r

(a) (b)

(c)

Fig. 5.12 System fault responses for different VSC2 controls.


- 157 -

5.5. Conclusions

The potential interactions between a STATCOM and a point-to-point VSC HVDC

link operating simultaneously in an AC system are analysed. Interactions are

identified both in the plant models and the outer controller loops between the two

components. A mathematical reduced network model is utilized in order to quantify

the degree of the plant model interactions, and the outer loop interactions are clearly

shown by means of modal analysis.

It has been demonstrated that the main factors that affect the degree of interaction

are:

i. The electrical distance between two devices,

ii. The strength of the connected AC system,

iii. The type of controls employed in the devices.

The interaction becomes most noticeable when the two components are located in

electric proximity with a very weak AC system. Under such system conditions,

adverse interactions between VSC HVDC and a STATCOM may occur. This is

specifically caused by a VSC in PQ control mode when the bandwidth of its P

control loop is tuned to be very high. For different VSC control strategies the AC

voltage control in a VSC also interacts with the STATCOM voltage control.

However, with properly tuned controllers, the STATCOM and VSC can work

coordinately during an AC system short circuit event.

Test on the dynamic GB system validates the results obtained from the reduced

network. However, as the dynamic GB system is in fact a very strong system with

high short circuit ratio, the degree of interaction between the STATCOM and VSC

HVDC is small. With well-tuned controllers, a good collaboration in voltage control

between the STATCOM and the VSC HVDC link is observed.

Chapter 6. Additional Control Requirements for VSC HVDC

- 158 -


Chapter 6. Additional Control Requirements

for VSC HVDC - A Specific Case Study

This chapter investigates the capability of VSC HVDC to restore local system power

balance using the two-area AC system with an injection VSC HVDC link initially,

considering the loss of a tie-line. The impact of generator controls is considered.

Adaptive power control schemes are proposed for the grid connected converter

when generation and demand imbalance occurs in the local system following a

major system fault event. Successful implementation of the proposed controls

enables the connected VSC HVDC links to improve power system stability. The

proposed control is then tested on the dynamic GB system model.

6.1. Power Balance between Generation and Demand

For normal variations of system demand and operating conditions in conventional

interconnected power systems, the balance between the mechanical power supplied

to generator prime movers and generator output electrical power is maintained by

the combined regulating reserve of all system units. However, when the condition of

quasi-equilibrium is upset by a major disturbance, such as the loss of a major tie-line

or a sudden change in the load demand, a severe generation/demand imbalance can

occur. Over short time frames (a few or tens of seconds), imbalances between

generation and demand are managed using frequency response services such as

turbine governing systems. Ways like load shedding and scheduled generator

tripping can be used for emergency situations. However, the problem with these

schemes is that the power mismatch in the system might not be exactly compensated


- 159 -

over a short time period, and the system can still be in the danger of instability. Over

longer time frames, balance between generation and demand needs to be rearranged

based on post fault generation dispatches and load flow scenarios, otherwise this

might result in unacceptable frequency excursions. In addition to conventional

methods, VSC HVDC is considered a potential solution to improve the situation of

power imbalance in local systems. However, before introducing any additional

controllers for VSCs, let us briefly review the principle of generation/demand

balance in the conventional power system.

Principle of Power Balance in Conventional Power Systems

The active power balance in the conventional power system is controlled by the

generators. A general expression for the power in a generator can be written as:

m e aP P P (6.1)

where Pm is the mechanical power supplied to the generators by prime movers, Pe is

the electrical power output of the generators, and Pa is the power accelerating or

slowing down the generators. Assuming a sudden decrease of the active power

consumption of the load (i.e. as a result Pe falls), the generator mechanical power Pm

will remain constant if no control actions are taken. An accelerating power will arise,

leading to an acceleration of the generator rotation speed and thus of the system

frequency (f). The frequency change in each of the generators in the system is

dependent on the variations in the kinetic energy (K) stored in the rotating parts of

the generator which is given as:

2 2 21

22

K J J f (6.2)

where J is the moment of inertia. Similarly, a sudden increase in the active power of

the load will lead to a deceleration of the generator rotation speed and also of the

system frequency.

On the other hand, the system voltage is mainly affected if reactive power imbalance

occurs in the system. For instance, consider a case of a simplified generator model

supplying a variable load as shown in Fig. 6.1 (a) with a lagging power factor cosφ.


- 160 -

The reactance of the generator is given by X and its internal emf is E. A sudden loss

of reactive power in the load will not affect the active power consumed in the load,

the mechanical power supplied to the generator, and its internal emf if no control

actions are taken. The power factor cosφ is increased and the magnitude of current is

decreased with the reduced reactive power in the load.

i1

i2

Vt1

E

ji2Xji1X

2φ

1φ

Vt2

Et

V 0

X

i

P,Q

(a) (b)

Fig. 6.1 Generator supplying variable load and voltage current phasors diagram.

The voltage and current phasors before and after the loss of reactive power in the

load are shown in Fig. 6.1 (b), labelled by subscript 1 and 2 respectively. It can be

observed that before any control actions have taken place, there is a sudden increase

in the magnitude of the generator terminal voltage as the voltage drop ji2X is reduced.

The opposite will happen if there is a sudden increase in the reactive power in the

load.

The above examples show how the frequency and voltage of a system can be

affected when the active or reactive power balance is broken. The immediate system

responses are illustrated before any control actions have taken place, which will help

to understand how VSC HVDC can be used to restore the power balance in the

system in the following studies.

System Power Imbalance with VSC HVDC

A specific case regarding a VSC HVDC supplied area being disturbed due to a

major system event is analysed. This is considered as a potential scenario where

additional controls are required from VSC HVDC to maintain system stability. In


- 161 -

this case study, the system dynamic behaviour following a fault event is presented,

and typical signals are identified as indicating power imbalance in the system and

can be used for enabling adaptive power controls in VSC HVDC links.

A schematic diagram is shown in Fig. 6.2 (a) as an example for such a situation. The

local system is originally supplied by a generator and a VSC HVDC link. The power

injected into this area is flowing into the local load demand and into the main grid

through a main transmission line. A power mismatch can occur in this local system

if the main transmission line is lost, due to a short circuit fault in the line or a sudden

change of load demand in the main grid. The turbine governor system in the local

generator can adjust its mechanical power input to match the new electric power

output after the fault. However, this method can be slow depending on the type of

the generation. The generator’s maximum mechanical power capability may be

insufficient if the power imbalance in the system is too large.

Additional power control in the VSC HVDC link may be used to quickly mitigate

the problem of power mismatch in this area. However, as VSC HVDC links are

normally operated at their maximum available power1, they are more useful in

situations where a power run back or power reversal is needed to reach a new power

equilibrium point in the system.

As shown in Fig. 6.2 (a), the original system power balance is written as:

m e Ex DC LoadP P P P P (6.3)

Considering the case when the middle line is disconnected due to a short circuit in

the line, then PEx = 0. Fig. 6.2 (b) depicts the system power imbalance situation as:

e_new DC Load

P P P (6.4)

m e_newP P

The amount of energy mismatch in the local system ∆E is different depending on the

speed of re-establishing the power balance in the system. The faster the power

1 For windfarm connected systems, the HVDC link would carry the maximum power available for the

windfarm. For interconnectors, the situation depends on contracted supply arrangements. In addition,

the overload power of converters is limited: power semiconductors have negligible thermal mass, so

the maximum power is about 1 p.u. unless this overload power rating is ‘bought’.


- 162 -

compensation is provided, the smaller the energy mismatch and the system is more

likely to be stable after the fault event.

SG

VSC HVDC

Link

External

GridTF

PLoad

Pe PEx

PDC

Pm

Turbine

Power

Loss of

loadLine

Break

Pm

1E 2

E

Pe_new

Power imbalance

occurs

Initial Power

drop

Different rate of Pe recovery

(by means of generator, VSC HVDC, etc)

Equal Area Curve

time

Amount of energy

imbalance

(a)

(b)

Fig. 6.2 (a) Diagram for specific case study and (b) Representation of power imbalance in the system.

Example Case

Such a situation is tested on the modified two-area test system with a VSC HVDC

link, as shown in Fig. 6.3 (there is only one tie-line between bus 7 and 8). The

purpose of this example is to investigate the dynamic responses of the power system

immediately following a major system fault event. Consider the worst case scenario

where the load in this local area is a static constant MVA load (motor driven) and

there is neither turbine governor nor VSC HVDC power support. The VSC HVDC

link is operated with VSC1 regulating the DC side voltage and VSC2 in constant

power control. The external grid is assumed to be a strong AC system represented

by an infinite bus that has enough capacity to take full power reversal in the DC link.

Details of the AC system can be found in Chapter 2. The generators have AVR and

PSS equipped.


- 163 -

400MW VSC HVDC link

PCC1

Ceq

G1

G2 G3

G4

110km

10km 25km

1 5

2 3

46

7

8

9

10 11

L7=1367MW

C7

L9=1767MW

C9

Two-area AC

network

Area1 Area2

VSC1VSC2

External Grid

PCC2400MW

700MW

700MW

400MW

719MW

700MW

VSC_AC2 VSC_AC1

Ceq

Fig. 6.3 Test system with VSC HVDC link.

A tie-line (line 7-8) disconnection event is applied at 2s. The initial power exported

from Area 1 to Area 2 (400MW and 100MVAr) drops to zero due to the line break.

The system responses are presented in Fig. 6.4.

1.5 2 2.5 3 3.5 4 4.5 5 5.50.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

Bus 7 Voltage

time(s)

V p

u

1.5 2 2.5 3 3.5 4 4.5 5 5.5

50

50.5

51

51.5

52

Bus 7 frequency

time(s)

f in

Hz

1.5 2 2.5 3 3.5 4 4.5 5 5.5-12

-10

-8

-6

-4

-2

0

Gen2 angle

time(s)

an

gle

in

de

g

Fig. 6.4 Test system responses for tie-line disconnection event.

According to the simulation results of the test system model in Fig. 6.4, the

following phenomenon is observed:

i. The system voltage and frequency start to increase until instability occurs after

5s. The phase angle at the generator bus 2 with reference to the slack bus is

also affected after the fault.

ii. At the instant of the fault event, both real and reactive power exported from

this local area is largely reduced. The generator rotor starts to accelerate


- 164 -

because of the decreased air gap torque. This acceleration will continue if the

imbalance between the generation and demand exists. The generator turbine

power does not change as no governor is applied. The generator terminal

voltages have a sudden increase due to the fact that the IX drop in the

generator winding decreases while the emf generated is the same. The voltage

continues to rise as there is more reactive power injected into the local system

than exported. However, the AVR equipped in the generators will act to bring

this voltage back to the set point value by reducing the excitation.

iii. Meanwhile, the VSC HVDC link is also affected by the fault event. The PCC

bus 7 voltage increases beyond the maximum VSC2 AC side voltage that can

be synthesised from the DC link after the fault. The voltage difference

between bus VSC_AC2 and bus PCC2 is shown in Fig. 6.5 left. It can be seen

that the VSC_AC2 bus voltage actually becomes lower than the PCC2 bus

voltage after 4.5s. Under such circumstances the power from the DC side does

not follow the normal rules for linear output AC voltage modulation and

transfer into the local AC system, causing the DC link power to be reduced

and reversed (Fig. 6.5 right). DC system instability is observed after 5s.

1 2 3 4 5-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05Voltage between Bus VSC2-AC and PCC

time(s)

V p

u

2 2.5 3 3.5 4 4.5 5 5.5-600

-400

-200

0

200

400

600

800

1000VSC2 Power

time(s)

P in

MW

Vdiff=VVSC2_AC-VPCC VSC2 Active Power

Fig. 6.5 VSC HVDC responses for tie-line disconnection event.

Restoring Power Balance by Generators

To address these problems, the turbine governors in the generators can firstly be

used to maintain system stability. Different types of turbine governing systems have

different response rates which can have an impact on the system’s stability. For

instance, hydraulic turbine governors are normally designed to have relatively large


- 165 -

transient droops and longer resetting times than steam turbine governors, and

therefore they have slower responses [20]. Considering the test system in Fig. 6.3

with steam or hydraulic type turbine governing systems equipped in all generators,

the input turbine power for the generators will drop at different rate when the

generator speed is accelerated. For the tie-line disconnection event, a comparison of

the effect of different governors on the system responses is presented in Fig. 6.6.

7. 005. 604. 202. 801. 400. 00 [ s]

52.

52.

51.

51.

50.

50.

7. 005. 604. 202. 801. 400. 00 [ s]

1. 5

1. 4

1. 3

1. 1

1. 0

0. 9

7. 005. 604. 202. 801. 400. 00 [ s]

467.

440.

413.

386.

359.

331.

Steam GOV

Hydro GOV

Unstable

Bus

7

freq

uen

cy H

z

Bus

7

volt

age

pu

VS

C2

Pow

er M

W

Fig. 6.6 System responses with steam and hydro type governors.

It is seen that steam type turbine governing systems provide a quicker turbine power

adjustment to restore power balance in the system, and thus the system is stabilized

following the event. The system with slower hydraulic governors cannot quickly

reach a new equilibrium point, which results in instability in the VSC HVDC link.

The simulation results obtained from the test system suggest that instability could

occur on both AC and DC sides of the system when power imbalance occurs under

situations of: (1) no control actions taken or (2) the control actions taken are not fast

enough. In the following sections, the capability of the VSC HVDC link to provide

power support to the grid is examined. Different types of controls schemes in the

grid connected VSC are proposed to meet the system stability requirements. The

effects of control parameter settings, system configurations and ramp rate settings in

the VSC are then addressed. To see the effect of the proposed controls in the VSC

HVDC clearly, generator governor models are removed.


- 166 -

6.2. Restoring Power Balance by VSC HVDC Action

The VSC HVDC connection itself has strong impact on the system stability. This is

especially true for high power import cases for a local area system. Severe frequency

deviations can occur under power imbalance conditions due to the fact that the

penetration of HVDC links, which are non-synchronous generators, replaces

conventional synchronous power plants. However, VSC HVDC systems also

provide the capability of fast and independent real and reactive power control, which

can be used to quickly reach a new equilibrium point for generation and demand in

the system. Based on the simulation results obtained before, the three signals in Fig.

6.4 (i.e. system voltage, frequency and phase angle) are strongly affected during the

fault event, and they can be considered as triggering signals for the grid connected

converter to control its power reference set point through a droop setting.

Droop Type Control for AC System Power Support

Droop control settings can be used in the grid connected converters to enable the

VSC HVDC link to contribute in maintaining system power balance. Some forms of

droop control structure has been seen proposed in [40, 106] for main grid frequency

support. In this case, any of the three signals (voltage, frequency or local angle) can

be used and their block diagram representation is shown in Fig. 6.7. With this

configuration, the active power reference set point is modified by the input signal

through a droop gain setting, as given by the following equation:

droopP f ,v, phi k (6.5)

where f, v and phi stands for the measured system frequency, voltage and phase

angle provided by phasors measurement units (PMU) devices.

f * ,V*, or phi*

P*

P

id*

Inner current

controlPI

f ,V, or phi

kdroop

Fig. 6.7 Droop type control to enable VSC HVDC for system power support.


- 167 -

The controls with different input signals are implemented in the test system (Fig.

6.3). An auxiliary signal is sent to the grid connected converter VSC2 modifying its

power reference set point when subjected to the tie-line disconnection event.

Different droop gain values are applied to show their effect on the system stability

performance after the fault.

Droop Control with Measured Frequency and Voltage as Inputs

The system responses are presented in Fig. 6.8 and Fig. 6.9 when the measured

frequency and voltage are used as the input signals. The case without the droop type

control is also presented in Fig. 6.8 which goes unstable after 5s. With the frequency

droop control applied, the system frequency deviation is detected by VSC HVDC,

which then starts to reduce its active power injection to reach a new equilibrium

point. For a small droop gain settings (fdroop=10), the power reduction in the VSC

HVDC is not fast enough and result in system instability after 6.5s. When the droop

gain is increased (fdroop=30), the system is stabilized after the fault event. Therefore,

in this case, the speed of power reduction in the DC link varies with the droop gain

value — the larger the droop gain value, the faster the power reduction.

7. 005. 604. 202. 801. 400. 00 [ s]

8E+2

5E+2

3E+2

0E+0

- 3E+2

- 5E+27. 005. 904. 803. 692. 591. 49 [ s]

1. 09

1. 06

1. 03

1. 00

0. 97

0. 94

7. 005. 604. 202. 801. 400. 00 [ s]

1. 8

1. 6

1. 4

1. 2

1. 0

0. 87. 005. 604. 202. 801. 400. 00 [ s]

53.

52.

51.

51.

50.

49.

Bus

7 f

requen

cy H

z

Bus

7 v

olt

age

pu

DC

lin

k v

olt

age

pu

VS

C2 P

ow

er M

W

fdroop=30 fdroop=10 no fdroop

Fig. 6.8 System responses with frequency droop control.


- 168 -

7. 005. 604. 202. 801. 40- 0. 00 [ s]

5E+2

4E+2

2E+2

9E+1

- 4E+1

- 2E+27. 005. 604. 202. 801. 40- 0. 00 [ s]

1. 1

1. 0

1. 0

1. 0

1. 0

1. 0

7. 005. 604. 202. 801. 40- 0. 00 [ s]

1. 4

1. 3

1. 2

1. 1

1. 0

0. 97. 005. 604. 202. 801. 40- 0. 00 [ s]

52.

51.

51.

50.

50.

50.

Bus

7 f

requen

cy H

z

Bus

7 v

olt

age

pu

DC

lin

k v

olt

age

pu

VS

C2 P

ow

er M

W

vdroop=1 vdroop=10

Fig. 6.9 System responses with PCC voltage droop control.

It is also the case when the measured voltage is used as the input signal. However, in

this case, both voltage droop gains (vdroop = 1 and 10) stabilize the system after the

fault event (Fig. 6.9). Again, a higher droop gain results in faster power change in

the VSC HVDC and less voltage and frequency deviations in the system.

Droop Control with Measured Phase Angle as Input

With rapid advancements in wide-area measurement system (WAMS) technology,

remote signals in the power systems are made to be available in local controls by

utilizing the synchronized PMUs. These PMUs are deployed at different locations of

the grid to get simultaneous data of the system in real time, and the PMU signals are

delivered at a rate up to 60 Hz [107, 108]. Therefore, with such a technique, it is

possible to use the measured phase angle as an auxiliary signal for modifying VSC

power reference settings. However, one potential problem claimed in [108] can be

the delay involved in transmitting the measured signal. Typical time delays can be

up to 1s, depending on the distance, transmission channel and other technical factors.

This is close to the time constants for the controls employed in the VSC HVDC link,


- 169 -

and possibly deteriorates the controllers’ dynamic performance. To incorporate the

delays in the model, a delay function is expressed as:

delaysT

delayG s e

(6.6)

Measured

SignalGdelay(s)

PMU at

Bus2

Local VSC

Cascaded Controls

Auxiliary

signal

Fig. 6.10 VSC control using PMU signal with time delay.

10. 008. 006. 004. 002. 000. 00 [ s]

5E+2

3E+2

1E+2

- 1E+2

- 3E+2

- 5E+210. 008. 006. 004. 002. 000. 00 [ s]

- 1. 1

- 5. 3

- 9. 6

- 14.

- 18.

- 22.

10. 008. 006. 004. 002. 000. 00 [ s]

1. 2

1. 1

0. 9

0. 8

0. 6

0. 510. 008. 006. 004. 002. 000. 00 [ s]

52.

51.

51.

50.

50.

49.

no phase delay phase delay 500ms phase delay 700ms

Bu

s 7

fre

qu

ency

Hz

Bu

s 7

vo

ltag

e p

u

VS

C2

Po

wer

MW

Bu

s 2

An

gle

deg

Fig. 6.11 System responses with PMU phase angle droop control considering time delay.

In this case, a PMU model is placed at the generator bus 2 and takes measures of its

phase angle with respect to the slack bus angle. This is sent to as an input signal to

the droop type control employed in VSC2. The simulation of the tie-line

disconnection event shows that the phase angle type droop control is also able to

modify the VSC output power and stabilize the system after the fault event without

considering the time delay in signal transmission. Variations in the droop gain value

have similar effects as the cases with frequency and voltage type droop controls.

However, when time delay in the signal transmission is considered (with the model


- 170 -

shown in Fig. 6.10), the performance of the controller appeared to be poor and was

even worse with increasing amount of delay. Fig. 6.11 presents the system responses

after the tie-line disconnection considering different PMU signal transmission delays

in the phase angle type droop control in VSC2. The system dynamic performance is

deteriorated with an increased delay time, which then goes unstable with a time

delay larger than 700ms.

Based on the simulation results for the droop type controls with different input

signals, a discussion is provided:

i. It can be seen that with a larger droop gain setting, the speed of power

response increases. Meanwhile, the magnitude of the oscillations in the DC

voltage also increases significantly (as shown in Fig. 6.8 and Fig. 6.9).

However, this is mainly due to the initial overshoots in the measured signals

when the fault occurs. Therefore, a low pass filter (LPF) may be required for

the measured signal to remove the initial overshoots as well as any higher

frequency oscillations. The figure below shows the input frequency with and

without a LPF when a droop type control is employed in VSC2 after the tie-

line disconnection. This can also be applied when voltage or phase angle is

used as the input signals.

0.99

1

1.01

1.02

0 2 4 6 8 10

time(s)

freq

uen

cy i

n p

.u.

measured

filtered

Avoid initial overshoots

Fig. 6.12 Effect of low pass filter for the measured frequency signal.

ii. For a relatively large droop gain value, the reference power set point of the

VSC HVDC varies with the measured signals, even in normal operating

conditions where very small fluctuations exist. This can result in undesirable

power oscillations in the VSC HVDC system in normal conditions.


- 171 -

iii. The droop gain needs to be properly tuned for different system conditions

depending on the plant model. For instance, the magnitude of frequency

deviation can vary with system inertia and fault events, which will then affect

the amount of power support provided by VSC HVDC. Although large droop

gain values increase the response speed of the VSC HVDC, they can also

deteriorate the DC system dynamic performance and lead to instability.

Proposed Control for Grid Power Support

In practice, voltage based droop controls are normally used as an auxiliary signal to

modify reactive power references instead of active power references. Also, the phase

angles in the system are always varying and it is difficult to keep track of the phase

angle difference between a particular bus where PMUs are installed and the slack

bus. Therefore, a modified control scheme proposed in this section is based on the

type of droop control using frequency measurements as the input to address the

problems raised before.

National Grid real time system frequency historic data suggest a normal frequency

fluctuation between ±0.1Hz. Fig. 6.13 shows the typical frequency data for a normal

month in 2014. With a large frequency droop gain value, very small fluctuations in

the measured frequency signal may cause undesirable power variations in VSC

HVDC. Therefore, the power reference set point should not be disturbed by small

frequency variations.

December 2014 National Grid System Frequency Data

Days from 2014-12-1 to 2014-12-31

Fre

quen

cy in

Hz

Fig. 6.13 National Grid frequency data.

Additionally, as mentioned before, the frequency deviation can vary with different

systems. This can have an impact on the selection of the droop gain value fdroop. For

power plants with the same technology, the inertia constant is generally proportional

to the rating, according to the data provide in [74]. Synchronous generators in


- 172 -

conventional power systems can contribute to this inertia. Renewable energy

generation such as windfarms, photovoltaic units and HVDC interconnectors that

are decoupled by the grid connected converters deliver little or even no inertial

response. Replacing conventional generation by renewable generation can result in

lower system inertia. However, in general, for the same amount of power imbalance

in the system, large systems usually have a higher inertia constant and consequent

lower frequency deviation in comparison with small systems. An example is given

in Fig. 6.14, which depicts the frequency change of the small two-area system and

the GB dynamic system for a same amount of power imbalance in the system. It can

be seen that the frequency rises much slower in the case of GB system. Therefore,

higher droop gain values (higher level of sensitivity) may be desired in the VSC

HVDC to provide full power support to the grid for large systems with smaller

frequency deviation.

Low inertia two-area system

High inertia GB system

Loss of 800MW load demand

50

50.2

50.4

50.6

50.8

51

51.2

0 2 4 6 8

Fre

qu

en

cy in

Hz

Time(s)

Fig. 6.14 Frequency change in different systems.

Based on the above analysis, the modified droop characteristics for a VSC HVDC

link is provided in Fig. 6.15.

Pref

f

Pdc_max

Pdco

-Pdc_max

Normal

Operating Point

dead-band

Only for VSC HVDC links

not operating at max rating

fdroop

Fig. 6.15 Modified frequency droop control.


- 173 -

A small dead-band characteristic of ±0.1Hz is included for the droop type control to

avoid active power oscillations due to small frequency fluctuations. A LPF is added

for the measured signals to remove overshoots and higher frequency oscillations,

which will reduce the level of oscillations in the DC link. The LPF GLPF(s) can be

represented as:

(s)LPF

1G

1 Ts

(6.7)

The dead-band characteristic can be achieved by using a look up table to determine

the reference power set points depending on the value of the input frequency signals.

The block diagram representation of this control is given in Fig. 6.16. High pass

filters may also be added to remove steady-state frequency offset in practical cases.

f P*

P

id*

Inner Current

ControlPI

P

Look-up table

GLPF(s)

Fig. 6.16 Block diagram representation of the modified frequency droop control.

An initial selection of the frequency droop gain can be made based on an estimation

of the frequency deviation in the system for a typical fault event. This can be

analysed by investigating the rate of change of frequency (RoCoF) [109]. A proper

droop gain value can enable VSC HVDC systems to provide their maximum power

support to the grid for a given frequency deviation.

When a fault event in the AC system occurs, the initial RoCoF is determined by the

amount of stored rotational kinetic energy in the system1. The rate of change of

power in the VSC HVDC is then jointly determined by the RoCoF and the droop

gain value. Therefore, since RoCoF cannot be controlled by VSCs, the value of the

droop gain needs to be properly tuned to ensure a fast enough response speed for the

VSC HVDC in face of system power imbalance situations.

1 Eventually other controls come into play, but the initial frequency deviation is set by inertia and

possibly fast power electronic units such as VSC HVDC


- 174 -

For an individual machine, the equation of motion is defined as:

a m e

dωJ T T T

dt (6.8)

2

0

1H Jω / VAbase

2 (6.9)

where

J = the moment of inertia,

ω and ω0 = angular velocity and rated angular velocity,

Ta,m,e = accelerating, mechanical and electromagnetic torque,

H = inertia constant,

VAbase = nominal apparent power of the generator.

Neglecting the losses in the unit, the equation of motion can be written as:

m e

dωJω P P

dt (6.10)

For multi-machine systems, neglecting the losses in the system, the equation of

motion can be summed as:

( ) ( )m e

dωJω P P

dt (6.11)

Substitute equation (6.9) into equation (6.11) gives:

_ _tot generation tot load2

0

2H VAbase dωω P P P

ω dt

(6.12)

The summation of the term H∙VAbase is essentially the total kinetic energy stored in

the system. Simplifying the above equation in per unit form and assuming ω≈1

results:

system

dω2H P

dt (6.13)

RoCoF

system

dω Pk

dt 2H

(6.14)

where Hsystem is the total system inertia constant.

The ROCOF is thus mainly determined by the amount of the power imbalance and

the total system inertia. Based on equation (6.14), the RoCoF of the system can be


- 175 -

estimated when subjected to a fault event that results in power imbalance. If the time

required for the VSC HVDC to react and provide its full power support to the

system is given as t, the system’s frequency deviation in that period can be estimated

as:

RoCoFf k t (6.15)

The estimated frequency change can help to set the initial droop characteristic. The

value of ∆f determines the upper and lower frequency limits for the VSC HVDC to

operate at its positive/negative maximum power ratings.

In application to the case before with the test system given in Fig. 6.3, considering a

typical power imbalance of around 400MW (400MW ≈ 0.28 p.u. on the base of

1400MW total generation in Area 1) and the total system inertia constant of H=13

consisting of two synchronous generators, the ROCOF is estimated as:

.. /

RoCoF

system

P 0 28k 0 01 pu s

2H 2 13

The bandwidth of the VSC HVDC power loop can be in a range between a few Hz

to tens of Hz. Therefore, a reaction time for the VSC HVDC of 0.5s to reverse its

full power is assumed. The estimated frequency deviation is then calculated as:

f 0.01 0.5 0.005 pu

This gives an estimated frequency droop design as shown in Fig. 6.17. The VSC

HVDC link is operated at its maximum power rating of 400MVA.

Pref p.u.

f Hz

P0 Pdco

-Pdc_max

Normal operating point

at maximum Power

50.1 f

49.9 f 49.9 50.1

Normal fluctuation

fdroop

1 2 3

5

4

Critical Points

Fig. 6.17 Estimated frequency droop characteristic.


- 176 -

Therefore, a frequency variation range of ±(0.005×50=0.25Hz) for the VSC HVDC

link to provide its full power is initially set. The critical values of the frequency

droop characteristic are listed in Table 6.1.

Table 6.1 Proposed frequency droop control settings.

Droop design Critical

Points

Frequency

in Hz

VSC HVDC

Power in p.u.

Low frequency point 1 49.65 1

Dead-band range

2 49.9 1

3 50 1

4 50.1 1

High frequency point 5 50.35 -1

In this case, for a system frequency higher than 50.35Hz or lower than 49.65Hz, the

VSC HVDC link operates in constant power mode. Fig. 6.18 presents the system

responses with the proposed control in VSC2 for the tie-line disconnection event. It

can be seen that the system is stabilized after the fault. The magnitude oscillation in

the DC side voltage is reduced in comparison with the responses shown in Fig. 6.8.

The VSC HVDC link provides its full power reversal with the designed droop

setting.

2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7

50

50.5

51

time(s)

Bus 7

fre

quency

2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7

-400

-200

0

200

400

600

time(s)

VS

C2 P

ow

er

MW

2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7

0.96

0.98

1

1.02

1.04

time(s)

DC

lin

k v

oltage

Fig. 6.18 System responses with modified frequency droop control.


- 177 -

6.3. Effects of Ramp Rate Limiter

Power reversal in VSC HVDC systems is achieved by reversing the direction of the

current instead of that of the DC voltage. It is claimed in [43, 110] that the VSC

HVDC transmission system does not have thermal/mechanical systems that are

affected by rapidly changing active power demand, and thus it provides the

capability of fast power run back and instant power reversal (i.e. the ramp rate is

theoretically only limited by the bandwidth of the power control loops from the

perspective of DC controls). Electrical inductance in the system does limit rate of

current change, but this is normally fast compared with AC system time constants.

Therefore, available power ramp rate in the VSC HVDC link is normally

constrained by the AC system strength, not DC controls. Some examples regarding

power ramp rate in VSC HVDC can be found in [12].

If a limitation is to be applied to the rate of power change in a VSC HVDC link due

to concerns in the AC system, a rate limiter can be added to the dq current reference

value, as shown in Fig. 6.19.

u=id* y=id_limited

Rate limit signal

Rate limiter

x

Fig. 6.19 Rate limiter for d-axis current reference.

The rate limiter with an internal variable x is defined as:

limit

slimit

limit limit

s s

limitlimit

s

u xrate

Trate

u x u xx rate rate

T T

rate u xrate

T

(6.16)

y x (6.17)


- 178 -

In this case, an emergency rate limiter of 1GW/s and a reduced rate limiter of

500MW/s are assumed to be applied in the VSC HVDC link. The power response of

VSC2 with a frequency droop gain of 30 (Fig. 6.8) is affected by the rate limiter as

presented in Fig. 6.20.

-600

-300

0

300

-1 1 3 5 7

No rate limit

rate limit = 1GW/s

rate limit =

500MW/s

VS

C2 P

MW

Time(s)

Fig. 6.20 Comparison of VSC2 power responses with the effect of rate limiter.

It is seen that the output power from the DC link is not affected when the emergency

rate limit of 1GW/s is used. When a slow rate limiter (500MW/s) is applied, the rate

of change of power exceeds these limitations. As a result, the power can only change

at the limited rate. Therefore, in the case that a rate limiter is required (from the AC

system point of view) in the VSC HVDC link, its effect needs to be taken into

consideration when designing a droop based adaptive power controller.

6.4. Restoring Power Balance Using VSC HVDC in Dynamic GB

System

By linking to other countries’ transmission systems, National Grid has increased the

diversity and security of energy supplies in UK. Apart from the IFA and the BritNed

interconnectors, which are already in operation in the south of England, a number of

new interconnector projects are proposed in the south of England. The 2014

National Grid Ten Year Statement lists a few of the links which are in the proposal

shown in Table 6.2.


- 179 -

Table 6.2 Interconnector projects in South England.

HVDC

Interconnector Location Rating Commissioning

Nemo link England - Belgium 1000MW 2018

IFA2 England - France 1000MW 2019

ElecLink England - France 1050MW 2016

FABLink France, Alderney and UK 1400MW 2020

The connection of multiple HVDC links in a local area can have significant impacts

on the system stability as studied before. To investigate potential stability problems

associated with future GB grid, a scenario is created based on the dynamic GB

system with three VSC HVDC links rated at 1.2GW being connected to the South

part of the system (bus 26-28). The other ends of the three DC links are connected to

infinite AC buses representing other strong AC systems, which have enough

capacity to take full power reversal in the VSC HVDC links.

27

26

2829 C

NN C

1 2

C

H

3

F

4

5

N 6

WF

7

8N

9 10

C11

N

15

F

12

13 14

C

16

C

1917

C

2022

21N

C

C

F

18

F

23

24

25

F C

H

VSC1

VSC2

VSClink3

VSClink2

VSClink1

VSC3

1GW

1GW

1GW

Phase

Reactor

Hydro

OHL

Bus

Transformer

Load

& Shunt

H

C

N

F

WF

CCGT

Nuclear

Fossil

Wind

Farm

Fig. 6.21 Interconnectors in dynamic GB system.

It is assumed that all three links are operated at 1GW, which is not their full power

rating, leaving a headroom of 200MW. A new load flow with the addition of the DC


- 180 -

links is satisfied by the method of distributed slack by load, which is an option of

balancing the power flow by means of a group of loads. Under such assumptions,

the active power of the selected group of loads will be modified so that the power

balance is once again met, while leaving the scheduled active power of each

generator unchanged. An overview of the system scenario is provided in Fig. 6.21. It

should be noted that there are two DC links importing power, while one is exporting

as indicated in the figure.

Based on the frequency deviation estimation method, frequency droop type controls

are employed in the three grid connected converters (VSC1-3) with properly tuned

drop gain values. Considering a case where DC link 1 and 3 are importing power

while DC link 2 is exporting power, the developed control schemes result in a

characteristic shown in Fig. 6.22, where the dead-bands and frequency droop

characteristics are included. Since the power headroom allowed in each VSC HVDC

link is small (200MW), their “overloading” capability (e.g. import or export power

larger than its rated value) is limited. Their main capability is to perform power run

back or reversal when required. Applying the designed control strategies to the grid

connected VSCs, DC link 1 and 3 is able to reduce the importing power when the

generation is larger than the load demand in the system, while DC link 2 is able to

reduce the exporting power when the generation is smaller than the load demand.

Detailed parameters for the proposed control schemes are given in Table 6.3.

Pref / MW

f /Hz

Pdc1,3_max=1.2GW

+Prated = 1GW 200MW

head room

Importing

Exporting

Pdc2_max=1.2GW

-Prated=-1GW 200MW

head room

DC link 1,3

DC link 2

Fig. 6.22 Designed control schemes for three grid connected converters.


- 181 -

Table 6.3 Detailed parameters of the designed control schemes of the grid connected converters.

VSC HVDC link 1,3 VSC HVDC link 2

Frequency

in Hz

DC Power in

p.u.(base 1GW)

Frequency

in Hz

DC Power in

p.u.(base 1GW)

49.5 1.2 49.5 1

49.9 1 49.7 1

50 1 49.8 0

50.1 1 49.9 -1

50.2 0 50 -1

50.3 -1 50.1 -1

50.5 -1 50.5 -1.2

In this case, the generation units in the system have turbine governing systems

equipped. Due to the meshed connections between the buses in South England

(buses 18-29), it is difficult to separate a local system from the main system by

tripping a single line — each bus is connected to the rest of the system with more

than 2 lines and the power can always flow between buses through other intact lines.

As a result, the situation of power imbalance and angular instability in the local

system after an event of line break is not likely to happen in the south part of this

dynamic GB system model.

Therefore, under such circumstances, load demand variation events are simulated in

the dynamic GB system for the area within the dashed line in Fig. 6.21 to create

imbalance between the system generation and demand. The total amount of demand

change is evenly spread across all the loads in the area. This includes a sudden loss

of 40% (circa 6.36GW) and a sudden increase of 30% (circa 4.77GW) of the total

load demand in this area. Due to the size of the system, only the simulation results of

selected system buses and generators, which are representative to reflect the

responses of the whole system, are presented. It should be noted that these events are

extreme cases and are only considered to show what functionality well-controlled

VSC HVDC is capable of.

Fig. 6.23 shows the system responses without the power support provided by the

VSC HVDC links. A sudden decrease of 40% of the load demand quickly raises the

system frequency and voltage, and system instability occurs after 15s even with the


- 182 -

help of the turbine governors in the generators. The DC links are in constant power

control which does not contribute to mitigating the power imbalance in the system.

15.12.9.36.23.10.0 [s]

50.37

50.27

50.18

50.09

49.99

49.90

15.12.9.36.23.10.0 [s]

1.252

1.158

1.064

0.970

0.876

0.782

15.12.9.36.23.10.0 [s]

2000.

1200.

400.0

-400.0

-1200.

-2000.

15.12.9.36.23.10.0 [s]

2.955

2.865

2.775

2.685

2.595

2.505

DC

lin

k p

ow

er

in M

W

Gen

erat

or

turb

ine

pow

er i

n M

W

Time(s)

DC link 3

DC link 2DC link 1

G5

G20G1, G10, G15, G25

Bus1

Bus5,10,15,25

Bus20,25

Bus1,5,10,15

Bus

freq

uen

cy H

zB

us

volt

age

pu

Fig. 6.23 System responses for a sudden decrease of 40% load demand in a particular area (VSC

HVDC links without designed frequency droop control).

Further tests enable the designed frequency droop controls in the VSC HVDC links,

and the system responses to a sudden 40% load decrease and 30% load increase are

depicted in Fig. 6.24 and Fig. 6.25 respectively. In case of a 40% load decrease, DC

link 1 and 3 perform fast power reversal. A small increase in the power exported by

DC link 2, from its rated value to its maximum value, also helps to mitigate the

power imbalance in the system. Similar behaviours are observed in the event of a 30%


- 183 -

load increase where DC link 2 performs fast power reversal while DC links 1 and 3

provide maximum power import. With the help of the power support provided by

VSC HVDC links, the system is stabilized after the fault events in both cases.

20.16.12.8.04.00.0 [s]

50.33

50.26

50.19

50.12

50.05

49.98

20.16.12.8.04.00.0 [s]

1.038

1.027

1.017

1.007

0.996

0.986

20.16.12.8.04.00.0 [s]

1186.

703.9

222.3

-259.3

-740.9

-1223.

20.16.12.8.04.00.0 [s]

2.943

2.894

2.844

2.795

2.746

2.697

DC

lin

k p

ow

er

in M

W

Gen

erat

or

turb

ine

po

wer

in

MW

B

us

freq

uen

cy H

zB

us

vo

ltag

e p

u

Time(s)

DC link 1,3

DC link 2

G5

G20

G1,G10, G15, G25

Bus1

Bus5,10,15,25

Bus1

Bus20,25

Bus5,10,15

Fig. 6.24 System responses for a sudden decrease of 40% load demand in a particular area (VSC

HVDC links with designed frequency droop control).


- 184 -

20.16.12.8.04.00.0 [s]

1221.

740.8

260.8

-219.2

-699.2

-1179.

20.16.12.8.04.00.0 [s]

2.988

2.935

2.883

2.830

2.777

2.724

20.16.12.8.04.00.0 [s]

50.01

49.95

49.89

49.83

49.77

49.71

20.16.12.8.04.00.0 [s]

1.018

1.004

0.991

0.977

0.963

0.950

DC

lin

k p

ow

er

in M

WG

ener

ato

r tu

rbin

e

po

wer

in

MW

Time(s)

DC link 1,3

DC link 2

G1

G5

G20

G10, G15, G25

Bus1 Bus5,10,15,25

Bus1

Bus25

Bus5,10,15

Bus20

Bu

s fr

equ

ency

Hz

Bu

s v

olt

age

pu

Fig. 6.25 System responses for a sudden increase of 30% load demand in a particular area (VSC

HVDC links with designed frequency droop control).

6.5. Conclusions

The chapter starts with the result of a dynamic simulation of an example test system

subjected to a major disturbance to illustrate the power imbalance problem in such

situations. The theory of the system behaviour when power imbalance occurs is

presented. It is identified that large power imbalance in the system may result in


- 185 -

system instability if the turbine governing systems equipped in the generators do not

respond fast enough. Under such circumstances, control methods are proposed for

grid connected VSC HVDC links to improve power system stability by quickly

changing their power output to help the system reach a new equilibrium point.

Based on the analysis of different input signals, a frequency based droop control is

proposed. To design the droop characteristic, the system frequency deviation under

power imbalance situations is estimated. It is demonstrated that both the value of the

droop gain and the ramp rate limit can affect the rate of power change in the VSC,

and both need to be taken into considerations in the design stage. The droop gain

value in the proposed frequency based droop control may need to be adjusted

depending on factors such as system conditions, the amount of power imbalance and

the total inertia in the system. Successful implementation of the proposed frequency

based control schemes demonstrates the effectiveness of using VSC HVDC to

provide additional power support in a future scenario based on the dynamic GB

system.

Chapter 7. Conclusions and Future Work

- 186 -


This chapter presents the conclusions of this thesis and recommendations for future

work.

7.1. Conclusions

The thesis identifies and investigates the potential problems and effects of having

VSC HVDC technology in the AC power system. In completing this research, an

assessment of the AC/DC control interactions is provided with the focus being put

on the electromechanical transient performance.

A brief review of the development of HVDC and past research on the integration of

VSC HVDC into conventional AC system is provided in this thesis, from which

potential problems and gaps within the related areas are raised. The issues regarding

the incorporation of VSC HVDC into AC system mainly fit into three aspects,

namely: (1) AC/DC modelling, (2) VSC HVDC-AC system control interactions and

(3) VSC HVDC-FACTS control interactions. To tackle the identified problems and

fill the gaps to date for the research in this area, several targeted studies have been

carried out within the thesis. These are summarized as:

i. Development of generic integrated AC/DC system models.

ii. Development of dynamic GB system with greater fidelity.

iii. Comparison of control strategies employed in VSC HVDC links and MTDC

systems and their effects on AC system stability.

iv. Identification and analysis of control interactions between VSC HVDC and

STATCOM.


- 187 -

v. Analysis of additional control capability of VSC HVDC links for main grid

active power support.

The outcomes of these five studies are the original contributions of this thesis. The

issues raised from the potential aspects have been fully addressed with further work

that has been undertaken in some of the areas. Details regarding the contributions

made by each of the studies to the problems of concern are addressed in the

following sections.

AC/DC Modelling

To study AC/DC control interactions, generalized integrated AC/DC models have

been developed. The modelling of the key components and the associated controls in

the AC and DC sides of the system has been described in detail. However, integrated

AC/DC system models for power system stability studies are often based on

simplified AC or DC side models. Even though detailed integrated models are seen

in some of the publications, the integration method has also not been addressed in

detail at the time of study. Therefore, a mathematical integration method is proposed

that is the first original contribution in this thesis. Instead of having one side of the

system to be modelled in a simplified way, the full VSC HVDC and AC system

models for power system stability studies are used. This includes the plant models

and controls of the converters and AC system generators. The method allows the

VSC models to be developed separately by considering them as current injections

into the connected AC system, and it therefore provides an alternative for quickly

integrating new VSC models into conventional power system models.

Following the development of generic AC/DC system models, another original

contribution made in this thesis is the development of a dynamic GB system model.

The developed model is based on a steady-state, representative load flow data of the

GB transmission network with the intention of testing probable future scenarios with

greater fidelity. The design of the generator controls (i.e. AVR, PSS and GOV) is

shown in a step-by-step procedure, and the method to modify the developed system

into other loading conditions is also provided. The form of the resulting dynamic

system has been designed to represent the main bottlenecks for inter-area power


- 188 -

transfers, retaining the parameters (impedances and ratings) of the real circuits

through those bottlenecks, but reducing the electrically close substations to

representative clusters. The significance of constructing this dynamic model lies

upon allowing exploration of a more realistic system as well as its related stability

and control issues. The detailed construction procedures as well as the full system

data have been included in this thesis, which provides a method of converting a

steady-state model into a dynamic model and also allows reproducing the system.

The AC/DC interaction studies that based on this more realistic large power system

model help to ensure that the exploration of the fundamental phenomena is

representative of practical system implementations to a greater extent.

VSC HVDC – AC System Control Interaction

The approaches of past research to the control issues of integrated AC/DC system

tended to view the problem with an emphasis on either the AC system or the DC

system, with consequent simplifications of the other side. This has the risk of

ignoring some potential control interactions in between. In this thesis, a holistic

approach was taken that utilized a detailed AC/DC modelling methodology and

control designs. As there is no available study that compares the effect of VSC outer

controls on the AC/DC system dynamic performance, a systematic assessment of

VSC controls is provided. The outcome of such a study provides recommendations

for the selection and tuning of the controls for VSC HVDC, which can improve the

AC system stability. The influence of a 4-terminal DC system control settings on the

DC system power flow and the resulting AC system dynamics is also described. In

this respect, the next original contribution of the thesis presents both a novel

methodology for controller analysis and a new set of controller configuration

recommendations.

To be more specific, the AC system inter-area oscillation is mainly affected by the

operating point of the DC link (power flow) and the VSC AC voltage control.

Installation of a paralleled VSC HVDC link usually affects the damping of the

connected AC system inter-area mode, which not only depends on the AC system

structure but also on the type of controls employed in the converter terminals.


- 189 -

Another major conclusion is that a fast acting AC voltage regulation at the receiving

end of the VSC HVDC link reduces the damping of the low frequency inter-area

mode, whereas it would improve damping at the sending end.

Analysis of the MTDC control strategies shows that the adopted MTDC control

scheme can significantly affect the DC power flow and thus lead to different

corresponding AC system responses. Constant DC voltage control with voltage

margins provides satisfactory integration of small scale AC-MTDC systems. The

responsibility of DC voltage control can only be transferred but not shared. It is

recommended that for large DC grid integration, droop controls between DC system

voltage and power should be used. It is demonstrated that droop control

characteristic in the DC grid allows balanced AC/DC dynamic performance and

flexible DC grid power control capability, which can be used to achieve an optimal

power injection scenario for the connected AC system.

In order to fully utilize the potential of the VSC HVDC, a frequency based droop

control method is proposed in this thesis to enable the active power support function

of VSC HVDC links together with the control design method. Successful

implementation of the proposed control schemes demonstrates the effectiveness of using

VSC HVDC to provide additional power support. However, affecting factors that need

to be considered in the controller designing stage (i.e. droop gain setting and ramp rate

limit) are addressed.

VSC HVDC - FACTS Control Interaction

The last original contribution made in the thesis addresses the potential control

interactions identified between VSC HVDC and STATCOM. Interactions are

identified in both the plant models and their outer controller loops, considering factors

such as the electrical distance between the two components, the strength of the

connected AC system and the type of controls employed. Due to the cascaded

control structure of VSC and STATCOM, a method combining relative gain array

and modal analysis techniques is used to address interactions occurred at multiple

levels. Adverse control interactions are identified when the two components are

located in electric proximity with a very weak AC system. In such conditions, the


- 190 -

STATCOM AC voltage control can be deteriorated by a closely located VSC real

power control with very high bandwidth.

The validation of the interaction study in the dynamic GB system shows a good

collaboration between a VSC HVDC link and a STATCOM operating in electric

proximity. This is due to the fact that the GB system is a strong system with high short

circuit power ratios, and thus the controls in the STATCOM and the VSC are well-

decoupled.

7.2. Future Work

The objectives of this research have been met by the work presented in this thesis.

However, the studies also suggest a number of areas where further work can be

carried out. The following are recommendations of possible future work worth

pursuing.

Effects of MTDC Systems on AC Networks

As the trend of HVDC development is expanding towards MTDC grid, the power

flow in the DC grid will become more complex and so will the controls in the

converter terminals. It is shown in this study that (1) the power flow in the VSC

HVDC link and (2) the AC voltage control employed in the converter terminals have

the most significant effect on the AC system inter-area oscillation. Therefore it is

necessary to do further work in order to address:

i. The effect of MTDC system optimal power flow scheme not only on the DC

system dynamic performance, but also on the AC system electromechanical

oscillations if such a problem is of concern.

ii. The coordinated tuning of AC voltage control when it is employed in multiple

grid connected converters as both the parameter settings and the location of

the control can substantially affect the AC system inter-area oscillatory

behaviour.

Furthermore, similar to the automatic generation control in the conventional AC

systems, optimal power flow in a MTDC system may require properly designed

power flow reference orders for all interconnected converter stations. Advanced


- 191 -

controls based on telecommunication technologies may be required to cooperate

with local station control and to overcome conventional operational speed

limitations. Since telecommunications and controller architectures are intimately

linked, the impact of related constraints need be incorporated to develop a

“supervisory master control” that improves MTDC system performance and offers

robust and reliable services to AC onshore networks. A higher level control system

modelling is required.

Extended Interaction Studies

System level electromechanical control interactions between VSC HVDC and

STATCOM are analysed in this study. The analysis is carried out from the stability

point of view, and therefore very detailed and fast electro-magnetic transients are out

of the scope. To fully capture the adverse interactions of interest, more accurate

representations of the key components may be required. Further analysis requires

greater model fidelity with the focus being put on fast dynamics such as

electromagnetic transient interactions and signal harmonic distortions(e.g. There

could be some harmonic effects that might lead to some adverse interactions

between electrically close devices).

With the increasing installations of HVDC projects and the development of MTDC

systems, fast DC grid system wide control interactions between converters and

nonlinear interactions (e.g. converter protections, limits, switching controls etc.)

may arise. Potential interaction studies should also consider cases between different

converter stations or between converters and other FACTS devices (e.g. TCSC, SVC,

SSSC etc.). VSC HVDC systems for offshore windfarm connections need to

consider electromagnetic transient interaction between wind turbines and windfarm

side converter stations. To handle the increased penetration of power electronic

devices in the future power system, coordinated control strategies to avoid adverse

control interactions between the devices are necessary.

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Appendix A

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Appendix


Appendix A

Power System Stability Basics and Techniques

A1. Electromechanical Oscillations

Rotor angle stability depends on the ability to maintain equilibrium between the

electromagnetic torque and the mechanical torque in each synchronous machine,

after being subjected to small-signal or large disturbances. The power-angle

characteristics suggest the power output of a synchronous machine varies as rotor

angle oscillates [20].

Under steady-state conditions, the rotor speed remains constant due to the balance

between the mechanical and electrical torques. However, when the system is

perturbed by events such as load variations, short circuits, loss of generation, etc.,

the system equilibrium point will be varied, which leads to the acceleration or

deceleration of rotors according to their rotating motion characteristics. Furthermore,

as the angle difference between two generators varies due the unequal rotor speed,

oscillations of the power exchange between the two machines occur. The equation of

motion of a synchronous machine is given as:

2

2

0

2m e D r

H dT T K

dt

(A1)

In the above equation, H represents the inertia constant. The angular position of the

rotor in rad is denoted by δ. Tm and Te represent per-unit mechanical torque and

electrical torque respectively. KD is the damping coefficient in per-unit torque/speed

deviation.

The effect of the mechanical losses on rotor oscillation damping is usually small,

and they can be neglected under most practical conditions. For synchronous

Appendix A

- 203 -

generators without POD controls, the primary source of damping is provided by

damper/amortisseur windings, which have a high resistance/reactance ratio. In

transient state, a current will be induced in the damper windings by the air-gap flux

whenever the rotor speed differs from the synchronous speed. The induced current

will generate a damping torque, which will counteract the rotor speed deviation.

The change in electrical torque of a synchronous generator following a disturbance

comprises two components:

e S DT K K (A2)

The synchronising torque component Ks∆δ is in phase with the angle deviation,

while the damping torque component KD∆ω is in phase with the speed deviation.

Lack of synchronising torque induces aperiodic drift of the rotor angle, whereas

insufficient damping torque results in oscillatory instability, as shown in Fig. A1.

Practically, most small-disturbance instability is caused by the lack of damping, as

sufficient synchronising torque can be provided by excitation control.

Oscillatory instability Non-oscillatory instability

Fig. A1 Small-disturbance response of rotor angle (modified from [20]).

Based on equations (A1) and (A2), the classical single-machine infinite bus model

without considering field circuit dynamics, amortisseur dynamics and excitation

control, can be represented using the block diagram shown in the following figure.

Appendix A

- 204 -

SK

1

2Hs

0

s

DK

mT

eT

r

Damping

Torque

Synchronizing

Torque

Fig. A2 Block diagram of a classical generator model connected to infinite bus system.

The effects of the field flux linkage variation and the automatic voltage regulator

(AVR) on synchronising and damping torque components are analysed in [20]. At

oscillating frequencies higher than a certain value, the field flux variations due to ∆δ

induce a positive damping component. However, the AVR action can result in a

negative damping component and weaken the system damping, especially for high

generator outputs and high reactance values of the external system.

Generally, both synchronising and damping torques under the condition with and

without damping control can be calculated and compared in order to evaluate the

impact of the POD control on the system damping. This approach is particularly

suitable for the damping controls of local area oscillations. Adding a well-designed

PSS usually enables a large increase of the damping torque component. It should be

noted that the result of damping torque analysis should agree with that of the

eigenvalue analysis.

Power oscillation problems can be categorised into local oscillations and

global/inter-area oscillations [84]. Local mode oscillations are associated with the

rotor angle oscillation that swings against the rest of the power system. Local

problems can also refer to the oscillations between a few generators close to each

other. The frequency range of local modes is normally between 0.8 to 2.0 Hz.

Inter-area oscillations usually involve groups of generators oscillating against other

groups of generators, which can be far away from each other. Inter-area modes

usually have a frequency range of 0.1 to 0.7 Hz, lower than that of the local modes.

Appendix A

- 205 -

Normally, inter-area oscillations occur between two subgroups of generators which

are interconnected by weak tie-lines. However, for some very low frequency inter-

area modes, all the generator plants in the system may be involved. Unlike local area

modes, which require detailed modelling and analysis only in the vicinity of the

plant, the entire interconnected system may need to be represented in detail to

investigate inter-area modes. A fundamental understanding of inter-area oscillations

is well-documented in [93].

A2. Modal Analysis Basics

Modal analysis based on state-space representations is the most widely used

technique to investigate small-signal stability and to identify oscillating modes in

power systems. Dynamic behaviour of a power system can be represented using a

set of first-order differential equations shown in equation (A3) and (A4), where the

vector x refers to the state variables, and u is the vector representing the inputs to the

system.

,x f x u (A3)

,y g x u (A4)

By linearizing the system based on an equilibrium operating point, the state-space

representation of a dynamic system can be obtained as:

x A x B u (A5)

x A x B u (A6)

The eigenvalues of the system, denoted as λi, are the solutions of the following

equation:

( )det I A 0 (A7)

By using the transformation shown in equation (A8), where coefficients z are

defined as the modes of oscillation. Φ is the modal matrix of A.

Δx Φz (A8)

Appendix A

- 206 -

Consequently equations (A5) and (A6) can be transformed to a set of uncoupled

state equations:

1z Λz Φ BΔu (A9)

Δy CΦz DΔu (A10)

The time response of the ith

state variable is given by:

1 2

1 2( ) ntt t

i i 1 i 2 in nx t ψ Δx(0)e ψ Δx(0)e ψ Δx(0)e (A11)

where 𝜙i and ψi represent the right and left eigenvectors respectively. It can be seen

that the free response of the system at that operating condition is represented by a

linear combination of n dynamic modes, where each mode has a corresponding

eigenvalue. The scalar ψiΔx(0) gives the magnitude of the excitation of the ith

mode.

The mode shape, which represents the relative activity of the state variable in a

particular mode, is given by the right eigenvector (in equation (A8)). The mode

shape technique is widely used to determine the input signals to the damping

controllers.

The stability of the system is assessed by evaluating the eigenvalues. A real

eigenvalue represents a non-oscillatory mode, while a pair of complex eigenvalues,

as shown below, corresponds to an oscillatory mode. The damping of the mode is

mainly determined by the real part the eigenvalue, and the oscillating frequency is

given by the imaginary part.

j (A12)

The damping ratio and the frequency of oscillation of the mode are expressed as:

2 2

,2

f

(A13)

The decaying rate of the amplitude of the oscillation is determined by the damping

ratio ξ. To demonstrate the graphical pattern of eigenvalues, an illustrative

eigenvalue plot is shown in Fig. A3, where the damping ratio for each mode equals

the corresponding value sinθ. Generally a POD control is designed to increase the

damping of both the unstable modes and the critical modes of interest. Meanwhile,

the POD control should not adversely affect the damping of other critical modes.

Appendix A

- 207 -

j

Inter-area

mode

Local modes

High bandwidth

modes

Unstable mode

Increase

Damping

Fig. A3 Eigenvalue plot example.

Participation factors, which are based on a combination of right and left eigenvectors,

are appropriate indications of the relative participation of the respective states in the

associated modes. They are commonly used to distinguish inter-area modes and

local modes, and they help to select feedback signals for POD controllers. Generally,

the state variables that have high participation factors in the critical modes are of

particular interest. An inter-area mode usually involves participation of a large

number of state variables from multiple generation groups.

The matrix CΦ is called observability matrix, which determines the relative

contribution of the respective modes to the observed system outputs. If the feedback

signal of a system is not appropriately selected, some poorly damped modes may not

be observable, and thus the POD controller cannot provide satisfactory damping to

these modes, especially for the inter-area modes. Therefore, the monitored quantities

from the system should have high observability, particularly with respect to the

poorly damped low-frequency modes.

Another commonly used technique in POD control design is the residue analysis,

which relies not only on the eigenvectors but also on the input and output matrices.

For an open-loop transfer function extracted from a multi-input multi-output system,

as shown in equation (A14). The residue at the pole λi is defined as Ri, and it

represents the relative weight of the mode in the respective output.

Appendix A

- 208 -

1

( )n

i

i i

RG s

s

(A14)

The feedback signals are required to enable a large residue relative to the target

mode, in order to obtain sufficient controllability over the mode of oscillation that is

to be damped.

A3. QR Method

To understand the QR method [90] for eigenvalue calculations, there are a few

basics that need to be specified:

i. In the QR method, R is an upper triangular matrix and Q is an orthogonal

matrix which satisfies:

11 12 1

22 210

0 0

n

nT

nn

a a a

a aQ Q and R

a

(A15)

If a matrix is a diagonal or triangular matrix, the eigenvalues of this matrix are

the diagonal elements. If the state matrix A can be transformed into such a

form, then the eigenvalues can be picked up.

ii. Similarity transforms which have the form of A’=BAB

-1 will not affect the

eigenvalues. In other words, A and A’ have the same eigenvalues. In the case

that B is orthogonal, the similarity transform can also be expressed as

A’=B

TAB

iii. Eigenvalues can be calculated through QR iteration which requires QR

decomposition at each iteration. These two key processes are explained here.

QR Iteration

Eigenvalues can be found using iteratively the QR-algorithm, which will use the

previous QR decomposition. Given a state matrix A, its QR decomposition is a

matrix decomposition of the form:

A QR (A16)

Appendix A

- 209 -

Using this as the initial value, a new matrix for iteration can be defined as:

2A RQ (A17)

This new matrix can be QR factorized as:

2 2 2A Q R (A18)

This process can be repeated by creating new matrices, e.g. A3=R2Q2, which can be

factorized into A3=Q3R3. At the kth

step, a matrix Ak can be defined by equation

Ak=Rk-1Qk-1 from the previous factorization of Ak-1. Matrix Ak will tend toward a

triangular or nearly triangular form whose eigenvalues are the diagonal elements.

This is because that the matrix Q of QR decomposition is orthogonal, so that the

iteration process is in fact:

2

T

T

A QR and R Q A

A RQ Q AQ

This is a similarity transform. The resulting new matrix Ak will have the same

eigenvalues as the original state matrix A. With a large number of steps k, the

diagonal elements of Ak will converge to the original eigenvalues of state matrix A.

QR Decomposition

There are different methods to compute the QR decomposition of the state matrix A,

such as the Householder transform, the Givens rotations and the Gram-Schmidt

orthogonalisation. The first method “Householder transform” is briefly discussed

here. The construction of Q and R is based on a series of orthogonal householder

matrices P1,P2,…Pn-1 that satisfy Pn-1…P2P1A=R, where R is an upper triangular

matrix. This idea can be expressed as a process that continues until an upper

triangular matrix R is obtained:

11 12 1 11 12 1

21 22 2 22 2

1 1

1 2 2

0

0

n n

n n

n n nn n nn

A A A A A A

A A A A AP A P

A A A A A

Appendix A

- 210 -

11 12 13 1

11 12 1

22 23 2

22 2

2 1 2 33 3

2

3

00

0 0

00 0

n

n

n

n

n

n nn

n nn

ˆ ˆ ˆ Â A A AA A A ˆ ˆ Â A A

A Aˆ ˆP P A P A A

A Aˆ Â A

11 12 1

22 2

1 2 1 1 2 10

0 0 0

n

Tn

n n

nn

A A A

A AP P P A R and P P P Q

A

During this tridiagonalization process, each householder matrix Pk can be calculated

using the householder transformation. The householder transform is to find a set of

transforms that will make all elements in one column below the diagonal vanish, and

then Q and R can be calculated to create the new state matrix A for the next iteration.

A4. Lead-lag Compensator

The lead-lag compensator is designed to add phase lead/lag to the system output. It

has a typical form of:

( )pz

p z

sleadlag k k

s

(A19)

The lead-lag compensator contains a single pole and a single zero where ωp and ωz

are the corresponding frequencies. It provides phase lead if the zero is closer to the

origin than the pole (i.e. ωz< ωp), or phase lag if the pole is closer to the origin than

the zero (i.e. ωz> ωp). When designing the compensation, the lead-lag compensator

can be expressed in a slightly different format as:

1

1

Tsleadlag k

αTs

(A20)

The lead-lag compensator is able to provide phase lead/lag at a particular frequency.

With the above expression, some characteristics of the phase lead-lag block design

are summarized:

Appendix A

- 211 -

i. Upper and lower cut-off frequencies:upper lower

1 1f and f

T T

ii. Frequency at where the maximum compensated phase occur: m

1

T

iii. Maximum compensated phase angle : max

11

arcsin( )1

1

An example bode plot of a typical lead (α =0.5 and T=0.2) compensator is shown

below:

0

2

4

6

Magnitude (

dB

)

10-1

100

101

102

0

5

10

15

20

Phase (

deg)

Bode Diagram

Frequency (rad/s)

7.07 ( / )m

rad s

max19.47

10 ( / )upper

rad s

5 ( / )lower

rad s

Fig. A4 Bode plot of an example lead compensator. Equation Chapter 1 Section 1

Appendix B

- 212 -

Appendix B

VSC Topologies, Losses and Capability

B1. Converter Topology

HVDC Light was first introduced by ABB in 1997. At the time it was a state-of-the-

art power system designed to transmit power underground, under water, and also

over long distances. It was claimed that this technology increases the reliability of

power grids by extending the economic power range of HVDC transmission from a

few tens of megawatts to 1200 megawatts at ±500kV. Examples include the first

commercial project “Gotland HVDC Light”.

The converter topology shown below is a two-level converter which is used in the

first and the third generations of HVDC Light.

Stack of IGBT

valves

Phase reactor

DC capacitor

Fig. B1 three-phase two-level converter [2].

Each valve consists of a stack of series and parallel connected IGBTs with anti-

parallel diodes. The number of series connected devices varies for different voltage

and current rating requirements. Typically, extra grading components are added to

the series connected IGBTs to ensure voltage sharing.

Considering one phase at a time, the converter output voltage can be ±Vdc/2, when

an upper valve conducts or a lower valve conducts respectively. By applying a

pulse-width modulation (PWM) control scheme to the converter, the output

waveform of each phase becomes some form similar to Fig. B2.

Appendix B

- 213 -

Fig. B2 Output waveform of two-level PWM VSC.

A sinusoidal voltage output is achieved after filtering. The quality of the resulting

sine wave (the harmonic content) depends on the PWM switching frequency. There

is always a trade-off between high switching frequencies and converter switching

losses. A switching frequency of 1950Hz was used in the first generation of HVDC

Light. Such a frequency can remove low-order harmonics, and thus filters are only

required for higher order harmonics. This greatly reduces the footprint of a VSC

station in comparison with a traditional current source converter station.

The instantaneous control of phase angle and voltage amplitude is achieved by

changing the PWM pattern, while power flow reversal in VSC is achieved by

changing the direction of current rather than the DC voltage polarity. VSC HVDC is

also a self-commutated converter, and therefore it does not require an AC voltage

source for commutation. This enables VSC HVDC the capability to connect a weak

AC system such as an offshore windfarm.

The second generation HVDC Light used a modified three-level topology. After that,

ABB reverted back to the two-level converter topology in its third generation of

HVDC Light, but with a more advanced control scheme called “optimum PWM

(OPWM)”. OPWM is designed to control the fundamental converter voltage, and at

the same time optimizing the criteria for controlling the harmonics. It can selectively

eliminate low-order harmonics for a given power level and switching frequency, and

thus the switching frequency can be reduced. The 350MW ±150kV VSC HVDC

scheme between Estonia and Finland used this Optimum PWM control with a

switching frequency of 1050Hz.

Appendix B

- 214 -

The second generation voltage source converter topology produced by ABB is a

three-level diode neutral point clamped (NPC) VSC as presented below.

Fig. B3 Single-phase diode neutral clamped voltage source converter.

This converter topology gives three different levels of output: ±Vdc/2 and zero. The

output waveform of a single phase is shown in Fig. B4.

Fig. B4 Sinusoidal voltage synthesized from a three-level converter with PWM.

The three-level output allows the switching frequency to be reduced for less

converter losses without having worse output harmonics. However, this

conventional diode-NPC converter suffers from the unequal distribution of semi-

conductor losses and valve voltage imbalance. The most stressed valve will limit the

Appendix B

- 215 -

permissible phase current and switching frequency for the converter. These issues

lead to a modified active neutral point clamped (ANPC) VSC as shown in Fig. B5.

Fig. B5 Single-phase active neutral clamped voltage source converter.

The ANPC VSC is a NPC VSC with the addition of an active switch connected in

anti-parallel with the NPC diodes. The addition of the active switches gives more

switching states which allow the losses to be distributed more evenly. This allows an

increase in the power rating and switching frequency compared to NPC. An example

of this technique is the Murraylink and the Cross Sound Cable projects in 2002.

Cell 1

Fig. B6 CTL converter single line diagram (modified from [111]).

Appendix B

- 216 -

The fourth generation of ABB’s HVDC Light is a cascaded two-level (CTL)

converter consisting of several smaller two-level building blocks, also called cells,

which enables the creation of a nearly sinusoidal output voltage from the converter.

The output AC voltage is adjusted by controlling the cells’ output voltage in each

arm. For example, the output of cell 1 in Fig. B6 can be switched to be equal to the

capacitor voltage by turning T2 on and T1 off, or zero by turning T2 off and T1 on.

If both valves are turned off, the cell is blocked and the current is conducted only

through the diodes. Each cell is switched at a low switching frequency, typically

about 150Hz. But the effective switching frequency per phase is about 2N times the

cell switching frequency, where N is the number of cells per arm. e.g. for N=38 cells

per arm, the effective switching frequency per phase leg can be calculated as:

150×38×2=11.4kHz. This is in the range of 10 times the switching frequency of a

two-level VSC, indicating an excellent dynamic response.

Siemens and Alstom Grid have also developed their multi-level VSC HVDC

converter under the name of “HVDC Plus” based on modular multi-level converter

(MMC), and “MaxSine” respectively. These two converter technologies both

employ a similar topology. The MMC consists of six converter arms and each

converter arm comprises of a number of modules (Fig. B7). Each module output

voltage is equal to the capacitor voltage if the upper IGBT is on and the lower IGBT

is off, or zero if the upper IGBT is off and the lower IGBT is on. This enables the

converter phase voltage to be controllable with a smallest voltage step equal to the

module voltage, thus is a few kV. Similar to the CTL, each sub-module individually

switches in and out only once per cycle. Therefore, the switching frequency of each

sub-module is reduced to the fundamental frequency (though further switching may

be used).

MaxSine is a hybrid VSC technology which combines the advantage of low-pulse-

number converters with PWM, and the multi-level approach. The semi-conductor

switches are arranged to form the converter. The multi-level cells are used to

synthesise a desired voltage waveform to satisfy the requirements of either the AC

or the DC network.

Appendix B

- 217 -

The desired AC output voltage is achieved by controlling the ratio of the two arm

voltages within the phase leg. Fig. B8 shows that a nearly sinusoidal sine wave can

be produced with a much lower voltage step in comparison with the two-level or

three-level PWM converter mentioned before.

Fig. B7 Three-phase MMC topology.

Fig. B8 Sinusoidal voltage synthesized from a MMC.

With high number of modules per converter arm, the output harmonic content is

very low, and this means AC filtering is not necessary. The footprint of a VSC

converter station can be greatly reduced. For multi-level systems, appropriate

Appendix B

- 218 -

division of the DC voltage between the capacitors on each level needs to be

maintained.

B2. Converter Losses

The table below illustrates the improvements in the losses of different types of VSC

HVDC converter.

Table B1 Different converter type typical losses.

Converter technology Converter Type Typical losses

per converter

HVDC Light first generation Two-level PWM 3%

HVDC Light second generation Three-level ANPC 1.8%

HVDC Light third generation Two-level OPWM 1.4%

HVDC Light fourth generation CTL 1%

HVDC MaxSine Combined PWM and multi-level 1%

HVDC Plus MMC 1%

The HVDC Light losses are primarily estimated from [112], produced by ABB. The

estimated numbers for HVDC plus and MaxSine are both taken from [7], as their

designs are similar. With the evolution of converter topology, converter losses will

decrease due to, amongst other things, the reduced switching frequency. However, at

present, this is still higher than the conventional LCC, which is at 0.8% or so per

converter.

B3. VSC Capability Curve

There are mainly three factors that affect the real and reactive power capability of

VSC HVDC systems:

i. Maximum valve current (IGBT current),

ii. Maximum DC voltage,

iii. Maximum DC current.

According to the equivalent circuit that represents a grid connected MMC in Fig. B9,

the equations for the VSC output powers are:

2sin cos

/ 2 / 2

c pcc c c pcc

c c

TF s TF s

V V V V VP and Q j

X X X X

(B1)

Appendix B

- 219 -

From the above equations, the theoretical VSC PQ capability curve can be plotted as

shown in Fig. B10 left. The converter maximum real power is lower than the rated

MVA, allowing some degree of reactive power capability when operating at the

maximum real power. However, when the limitation factors are taken into

consideration, the PQ capability curve is modified as Fig. B10 right. The reactive

power capability is mainly dependent on the voltage difference between the PCC

bus voltage the converter AC side voltage. Therefore, the reactive power capability

will decrease with an increasing PCC voltage.

SM

SM

SM

SM

Ia

XsXTF

Xs

limb

reactor

Connection

Transformer

Vpcc

XTF Xs / 2

i

Equivalent

Circuit

Pc , Qc

Converter

side voltageAC side

voltage

pccV 0 c

V

Fig. B9 MMC based converter AC side equivalent circuit.

Real Power

Reactive Power

Rated Constant

MVA

Lagging

Leading

Pmax-Pmax

Ideal PQ Curve for MMC PQ Curve for MMC Considering Limits

Real Power

Reactive Power

Lagging

Leading

Maximum DC PowerPCC voltage in p.u.

Rated MVA

Vpcc=1

Vpcc>1

Vpcc<1

Maximum Current

Fig. B10 VSC HVDC capability curves.


Appendix C

- 220 -

Appendix C

AC and DC Model Equations

C1. Sixth Order Generator Equations

12

1 d dq q d d d d d ls d q fd

do d ls

X XdE E X X I X X I E E

dt T X X

22

1 q q

d d q q q q q ls q d

qo q ls

X XdE E X X I X X I E

dt T X X

1 1

1d d q d ls d

do

dE X X I

dt T

2 2

1q q d q ls q

qo

dE X X I

dt T

02

1

2

ref

m e

df

dt

dT D P

dt H

The algebraic equations defining the stator voltages and generator electrical real

power are given below, assuming that the generator armature resistance is negligible.

1

2

2 2

cos

sin

d ls d dq q d d d

d ls d ls

q ls q q

d d q q q

q ls q ls

e q q d d

q d

X X X XV V E X I

X X X X

X X X XV V E X I

X X X X

P V I V I

V V V

where all notations in the above equations are in consist of [113].

Appendix C

- 221 -

C2. Generator Saturation Characteristics

The saturation characteristics of a synchronous generator defined in DIgSILENT

PowerFactory is given by parameters SG1.0 and SG1.2. These parameters can be

calculated from the open circuit saturation curve which is normally the only

saturation data available. In this case, the example data listed below, which is

provided for the generators in the two-area system model, is used to demonstrate

how the saturation characteristic is defined. The data is given as:

Asat = 0.015 Bsat = 9.6 ψT1 = 0.9

Under no-load rated speed conditions, the open circuit characteristic relating

terminal voltage and field current gives the saturation characteristic. The saturation

curve can be divided into two segments: unsaturated segment I and nonlinear

segment II. The threshold value ψT1 defines the boundary for these two segments as

shown in the figure below:

I

1T

2T

ifd or MMF

air-gap line

slope = Ladu

Voltage or

flux linkageat

I II

12I

1T

ifd or MMF

air-gap line

slope = Ladu

Voltage or

flux linkage

1.0

1.2

10I

I0 I1.0 I1.2

(1) (2)

[p.u.]

Fig. C1 Open-circuit saturation characteristic (1) normal definition and (2) DIgSILENT definition.

For segment I, ψI = 0, the slope of the air-gap line Ladu is the unsaturated values of

Lad, which equals to 1.6 as given in [20].

For segment II, ψI can be defined by a mathematical function:

1( )sat at TB

I satA e

(C1)

However, the definition of the saturation curve in DIgSILENT PowerFactory is

different, as shown in (2) in Fig. C1. Its characteristic is given by specifying the

excitation currents I1.0 and I1.2, which are needed to obtain 1 p.u and 1.2 p.u of the

Appendix C

- 222 -

rated generator voltage under no-load conditions, respectively. Applying the

provided parameter values into the above equation gives:

1

1

(1 )

10

(1.2 )

10

0.04

0.267

sat T

sat T

B

I sat

B

I sat

A e

A e

Therefore I1.0 and I1.2 can be derived as:

10 121.0 1.2 0

1 1.2 10.65 0.917 0.625I I

adu adu adu

I I IL L L

As defined by DIgSILENT PowerFactory technique reference, the value of the

parameters for generator saturation characteristic in DIgSILENT PowerFactory is

calculated as:

1.01.0

0

1.21.2

0

1 0.039

1 0.2231.2

ISG

I

ISG

I

C3. Network dq0 Transformation

The transformation contains two parts: Clarke and Park transformations. In the case

of balanced three-phase circuits, application of the dq0 transform reduces three AC

quantities to two DC quantities. This simplifies the calculation in the system, and an

inverse transform is used to recover the actual three-phase AC quantities. The Clarke

transformation (alpha-beta transformation) for three-phase power system elements

has the form of:

0

1 11

2 2

3 30

2 2

1 1 1

2 2 2

a

b

c

v v

v k v

vv

(C2)

Appendix C

- 223 -

The three-phase voltages in a balanced AC system are given as:

( ) 2 cos( ( ))

2( ) 2 cos( ( ) )

3

2( ) 2 cos( ( ) )

3

a

b

a

v t v t

v t v t

v t v t

where v is the RMS value. In the case of k=2/3. Applying the Clarke transformation

gives:

2 cos ( )

2 sin ( )

0

v v t

v v t

v

This is equivalent to the phasor representations (vreal and vimaginary) of the voltages

which are commonly used in a balanced AC system. This is known as the magnitude

invariant transformation. Additionally, when k=√(2/3), the transformation results:

3 cos ( )

3 sin ( )

0

v v t

v v t

v

In this case the amplitudes of the transformed voltages are not the same, which is

different from the case of magnitude invariant transformation. This is referred to as

the power invariant transformation. To further transform the phasor representations

into DC components, the Park transformation is applied. The transformation and its

reverse form are given as:

cos sin

sin cos

d

q

v v

v v

(C3)

cos sin

sin cos

d

q

vv

vv

(C4)

Appendix C

- 224 -

where angle θ is the angle of a reference dq frame. This angle can be different in an

integrated AC/DC system model. The transformation between different dq reference

frames in a large AC/DC system is given below. Assuming a network frame (D-Q)

with reference angle θ, and a generator or a converter reference frame (d-q) with

reference angel 𝛼, we have:

(C5)

cos sin

sin cos

D

Q

v v

v v

(C6)

cos sin cos( ) sin( )

sin cos sin( ) cos( )

cos sincos sin

sin cossin cos

cos sin

sin cos

d

q

D

Q

v v v

v v v

v v

v v

v

v

(C7)

The above transformation allows conversions between different dq reference frames,

and thus dq domain calculations can be carried out throughout a large system model.

C4. Linearized VSC HVDC Link Equations

R+L

PCC2PCC1

CeqCeq

VSC1 VSC2

Vdc1 Vdc2idc

R+L

idc1 idc1

RdcLdc

VSC HVDC link

AC System

AC System

Fig. C2 Point-to-point VSC HVDC link.

The linearized converter model for a point-to-point VSC HVDC link used in the test

systems in this thesis is provided in this section. VSC1 is configured to maintain a

constant DC link voltage (feedback DC voltage control) and constant reactive power

Appendix C

- 225 -

Q = 0 (feedback Q control). VSC2 is configured for real and reactive power control

(feedback PQ controls). The inner vector current controllers take the form of

kdq(1+1/Tdqs). The outer loop controllers take the form of kp+ki/s.

The state equations for converter plant model are:

d d q d dLi Ri Li e v (C8)

q q d q qLi Ri Li e v (C9)

( )d d q q dc

dc

eq dc eq

e i e i IV

C V C

(C10)

The controller state equations are:

*( )dd d d

d

kx i i

T

*( )q

q q q

q

kx i i

T

* *

_ _( ) ( )dc i dc dc dc P i Px k V V or x k P P

*

_ ( )Q i Qx k Q Q

Four additional state variables are introduced for the controllers. The internal

variables can be expressed by equations:

*

*

( )

( )

d d d d d q d

q q q q q d q

e k i i x Li v

e k i i x Li v

* * * *

_ _

* *

_

( ) ( )

( )

d p dc dc dc dc d p P P

q p Q Q

i k V V x or i k P P x

i k Q Q x

Some other associated VSC HVDC link parameters are provided as:

i. DC lines parameters: Rdc=0.0113 Ω/km, Ldc= 0.466mH/km.

ii. Paralleled DC side equivalent capacitor is estimated as: Ceq = 150μF,

operating at ±320kV.

iii. Connection transformer Tc: 230kV/325.73kV with short circuit voltage 15%.

iv. Converter equivalent AC coupling phase reactors: R=0.005p.u., X=0.15p.u.

Appendix C

- 226 -

After linearization, the state space equation for VSC1 with feedback Vdc-Q control is:

_

***___

( ) 10 0 0

( ) 10 0 0 0

( )( )( )

2 (2

d p dcd d

q q

d

d d p dc dc d dc d d d dq p Qd p dc dc dcq

q Q q q q q qd dc d d d ddc

eq dc eq dcd

q

dc

Q

k kR k k

L L L L

R k k

L L Lii k k V k x k i x vk k Q Qk k V Vi

k x k i x v ik x k i x vV

C V C Vx

x

x

x

*

_ _

2

_

_

)

0 0 0 0

0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0 0

d

q

q p Q q p Q q Q q q q q q q q dcd d d

eq dc eq dc eq dc eq dc eq dc d

qp dc dd d

dcd d d

Qq q

d d

i dc

i

i

k k Q k k Q k x k i x v i k i Vi k i

C V C V C V C V C V x

xk kk k

xT T T

xk k

T T

k

_

_ _

_ _ _

_

_ _

_

_ _

0 0 0 0 0

0 0 0 0

1

0 0 0 0 0

0 0 0 0

0 0 0 0 0

0 0 0 0

d p dc

q p Q q p Q

q d p dc d q p Q q q p Q qd

eq dc eq dc eq dc eq dc eq dc eq

d p dc

d

q p Q q p Q

q q

i dc

i q i q

k k

L

k k k k

L L

i k k i k k i k k ii

C V C V C V C V C V C

k k

T

k k k k

T T

k

k k

*

*

d

q

dc

dc

v

v

V

Q

Q

I

Appendix C

- 227 -

The state space equation for VSC2 with feedback PQ controls is

***___

*

_

( ) 10 0 0 0

( ) 10 0 0 0

[ ( ) ]( )( )

2 [ ( )2

d d

q q

d

d d p P d P d d d dq p Qd p dcq

q Q q q q q q q p Qd P d d d ddc

eq dc eq dcd

q

P

Q

R k k

L L L

R k k

L L Lii k k P P k x k i x vk k Q Qk k P Pi

k x k i x v i k k Q Q kk x k i x vV

C V C Vx

x

x

x

2

_ _

]

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0 0 0

0 0 0 0 0 0 0

0 0

d

q

q Q q q q q q q q dcd d d

eq dc eq dc eq dc eq dc eq dc d

qd d

Pd d

Qq q

d d

d p P d p P

i

i

x k i x v i k i Vi k i

C V C V C V C V C V x

xk k

xT T

xk k

T T

k k k k

L

_ _

_ _ _ _

_ _

_ _

_ _

_ _

0 0 0

0 0 0 0 0

1

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

q p Q q p Q

q d p P d d p P d q p Q q q p Q qd

eq dc eq dc eq dc eq dc eq dc eq dc eq

d p P d p P

d d

q p Q q p Q

q q

i P i P

i q i q

L

k k k k

L L

i k k i k k i k k i k k ii

C V C V C V C V C V C V C

k k k k

T T

k k k k

T T

k k

k k

*

*

d

q

dc

v

v

P

P

Q

Q

I

Appendix D

- 228 -

Appendix D

Data for Developing Dynamic GB System

Detailed data and parameters needed to establish the dynamic GB system are

presented in this part together with the specifications of the techniques used during

the construction process. For more specific background data of the GB network

model, please refer to [71, 72].

Definition of tabulated GB system data

Abbreviations Definition

V Nominal Voltage

Pgen Effective generation in the reference load flow case

Qmax and Qmin Maximum and minimum reactive power capability for each

generation

Shunt gain/loss The supplied/absorbed reactive power of the installed switched

shunts in the load flow reference case

SVC Qlead and Qlag The reactive power capability of the installed SVCs

I2R ,I

2X

The active and reactive power transmission losses on the lines

within the reduced parts of the network

Bint Shunt gains from the lines on the reduced parts of the network

R,X,B Resistance, reactance, and susceptance of the transmission lines in

per unit values with a base of 100MVA

TF

Transformers that are placed in some branches and there are

quadrature boost transformers (QB TF) in double circuits 1-3 and

12-18 with 2 degree phase shifts for the load flow solution

Pload, Qload Active and reactive power of loads

Rating Winter peak transmission line ratings

WF Windfarm type generation

The frequency and time base for the following data is 50Hz and 1s respectively.

Appendix D

- 229 -

D1. Steady-state Data

Generation Data

Node Name V PGen Qmin Qmax

- - kV MW MVAr MVAr

1 Beauly 275 854.00 -254.76 244.45

2 Peterhead 275 1264.00 -491.03 1122.84

3 Errochty 132 780.00 -235.11 276.13

4 Denny/Bonnybridge 275 2337.00 -952.16 939.73

5 Neilston 400 882.00 -439.71 431.86

6 Strathaven 400 871.00 -527.79 476.55

7 Torness 400 2047.00 -805.33 1027.44

8 Eccles 400 0.00 0.00 0.00

9 Harker 400 0.00 0.00 0.00

10 Stella West 400 2817.00 -1507.36 1424.32

11 Penwortham 400 4576.00 -2249.66 2796.25

12 Deeside 400 3353.00 -1941.67 2000.93

13 Daines 400 0.00 0.00 0.00

14 Th. Marsh/Stocksbridge 400 0.00 0.00 0.00

15 Thornton/Drax/Egg 400 6271.80 -2527.87 3535.03

16 Keadby 400 9838.00 -5207.05 6007.62

17 Rattcliffe 400 1608.00 -405.94 814.23

18 Feckenham 400 1759.00 -607.75 924.99

19 Walpole 400 2614.00 -1631.68 1499.33

20 Bramford 400 1254.00 -286.74 857.78

21 Pelham 400 535.00 -306.07 326.15

22 Sundon/East Claydon 400 323.00 -232.68 189.72

23 Melksham 400 6180.00 -3015.93 3193.04

24 Bramley 400 0.00 0.00 0.00

25 London 400 1708.00 -947.42 949.38

26 Kemsley 400 4430.00 -1840.61 2520.08

27 Sellindge 400 1044.00 -541.79 737.03

28 Lovedean 400 1229.00 -650.91 718.62

29 SWP 400 1742.00 -892.46 858.67

Appendix D

- 230 -

Interconnectors

Interconnector Active power

capability

Active

power Shunt Gain Shunt Loss Pload Qload

- MW MW MVAr MVAr MW MVAr

27 - Sellindge 1988 Import

-2000 Export -1598.00 1040.00 -200.00 0.00 1200.00

26 - Kemsley 1320 Import

-1390 Export -964.00 780.00 0.00 58.30 33.40

5 – Strathaven1

80 Import

-500 Export 0.00 59.00 0.00

100.0

0 40.00

Shunt components data

Node Shunt Gain Shunt Loss SVC Qlead SVC Qlag Bint

- MW MW MVAr MVAr B % p.u.

1 27.00 0.00 0.00 0.00 132

2 0.00 0.00 -75.00 225.00 237.6

3 0.00 0.00 0.00 0.00 84

4 0.00 0.00 0.00 0.00 305

5 0.00 0.00 0.00 0.00 216

6 0.00 0.00 0.00 0.00 573

7 9.00 0.00 0.00 0.00 447.7

8 0.00 0.00 0.00 0.00 14.57

9 375.00 0.00 -142.76 334.06 22.08

10 684.00 -120.00 0.00 0.00 201

11 945.00 -220.00 0.00 0.00 581

12 328.00 -380.00 0.00 0.00 728

13 847.00 -240.00 0.00 0.00 254

14 199.00 -440.00 0.00 0.00 484

15 1030.00 -580.00 0.00 0.00 426.53

16 333.40 -320.00 0.00 0.00 333

17 574.86 -60.00 0.00 0.00 46.7

18 4454.00 -600.00 -358.27 1068.69 786.6

19 412.20 -120.00 0.00 0.00 272

20 287.40 0.00 0.00 0.00 83.3

21 495.00 -120.00 -141.28 341.02 114.29

22 2218.00 -300.00 -60.00 391.15 164.4

23 1170.70 -1080.00 0.00 240.00 1646.6

24 614.00 -120.00 0.00 0.00 16.67

25 2400.00 -2930.00 -337.12 694.06 4043

26 352.00 -180.00 0.00 0.00 362

27 110.00 0.00 -283.60 319.28 112

28 1140.00 -440.00 -203.18 341.02 468.6

29 1452.70 -380.00 -312.56 862.04 733.4

1 Interconnector 5 is not considered in the reference load flow case

Appendix D

- 231 -

Load data

Node Pload Qload I2R I

2X

- MW MVAr MW MVAr

1 468 102 22 140.5

2 513 113 30 307

3 555 105 44 158.4

4 1308 317 19.3 606.5

5 502 128 3.8 132.2

6 1276 315 27.4 512.7

7 745 171 8 325.9

8 117.5 37.4 1 6.7

9 130 53 4.9 139.4

10 2561 465 8 760

11 3360 760 53.4 1422.7

12 1189 338 20 774

13 2524 766 21 732.5

14 1831 566.5 12.5 499.2

15 2633 694.6 36 1207.8

16 1607 655 84.5 2734.6

17 1081 371 14.5 571.1

18 5362 1935 75.5 1732

19 2019 648 47.1 1093

20 1027.36 305.8 14 483

21 702 202.2 17 646

22 1820 665 41.8 833.1

23 4734 1337 47.4 1848.8

24 1418 528 5.9 366.7

25 9734 2902 70.7 2667.7

26 1424 434 26 992

27 457 138 5.8 221.7

28 2751 841 11 401.7

29 2577 356 25 567.7

Appendix D

- 232 -

Line data

Line data part 1

From To Circuit V R X B Rating TF QB

TF

phase

shift

- - - kV p.u. p.u. p.u. MVA - - -

1 2 2 275 0.0122 0.02 0.0856 525 No

1 3 1 275 0.007 0.15 0.052 132 Yes Yes 2.00°

1 2 1 275 0.0122 0.02 0.2844 525 No

1 3 2 275 0.007 0.15 0.052 132 Yes Yes 2.00°

2 4 1 275 0.0004 0.065 0.4454 760 No

2 4 2 275 0.0004 0.065 0.5545 760 No

3 4 2 275 0.003 0.041 0.0044 648 Yes

3 4 1 275 0.003 0.041 0.044 648 Yes

3 2 1 275 0.03004 0.077 0.0124 652 Yes

4 7 1 400 0.00211 0.0135 0.1174 1090 Yes

4 6 2 400 0.0013 0.023 0.1496 1500 Yes

4 6 1 400 0.0013 0.023 0.1758 1120 Yes

4 5 2 400 0.001 0.024 0.125 1000 Yes

4 5 1 400 0.001 0.024 0.125 1000 Yes

4 7 2 400 0.0021 0.0135 0.1538 1090 Yes

5 6 1 400 0.00085 0.01051 0.38254 1390 No

5 6 2 400 0.00151 0.01613 0.59296 1390 No

6 9 2 400 0.00078 0.00852 0.0737 2100 No

6 9 1 400 0.00078 0.00852 0.4635 2100 No

7 8 2 400 0.0004 0.0001 0.728 2180 No

7 8 1 400 0.0004 0.0001 1.2872 2500 No

7 6 2 400 0.003 0.2 0.2939 950 No

7 6 1 400 0.003 0.2 0.2939 950 No

8 10 1 400 0.00083 0.0175 0.6624 3070 No

8 10 2 400 0.00083 0.0175 0.6624 3070 No

9 11 1 400 0.00164 0.0163 0.4868 1390 No

9 11 2 400 0.00164 0.0163 0.4868 1390 No

9 10 2 400 0.00352 0.02453 0.1898 855 No

9 10 1 400 0.00492 0.0343 0.2502 775 No

10 15 2 400 0.00053 0.00835 5.373 4840 No

10 15 1 400 0.00052 0.0063 1.0636 4020 No

11 15 2 400 0.0007 0.042 0.3907 2520 No

*R, X, and B of the transmission lines are in per unit values with a base of 100MVA

Appendix D

- 233 -

Line data part 2


TF

phase

shift

- - - kV p.u. p.u. p.u. MVA - - -

11 15 1 400 0.00099 0.042 0.5738 2520 No

11 13 2 400 0.0004 0.0052 0.2498 2170 No

11 13 1 400 0.0004 0.0052 0.2664 2210 No

11 12 2 400 0.0001 0.0085 0.0798 3320 No

11 12 1 400 0.0001 0.0085 0.0798 3320 No

12 13 2 400 0.00096 0.01078 0.385 3100 No

12 18 2 400 0.00074 0.009 0.2911 2400 No Yes 2.00°

12 18 1 400 0.00097 0.009 0.3835 2400 No Yes 2.00°

12 13 1 400 0.00096 0.01078 0.385 3100 No

13 18 2 400 0.00049 0.007 0.1943 2400 No

13 18 1 400 0.00084 0.007 0.7759 2400 No

13 15 2 400 0.00137 0.023 0.6643 1240 No

13 15 1 400 0.00164 0.023 0.1104 955 No

13 14 1 400 0.00107 0.01163 1.1745 1040 No Yes 0

13 14 2 400 0.00082 0.01201 1.2125 1040 No

14 16 2 400 0.0005 0.016 0.2795 2580 No

14 16 1 400 0.005 0.018 0.1466 625 No

15 16 2 400 0.00033 0.0052 0.3534 2770 No

15 16 1 400 0.00016 0.00172 0.3992 5540 No

15 14 2 400 0.00019 0.00222 0.7592 5000 No

15 14 1 400 0.00018 0.00222 0.5573 5000 No

16 19 2 400 0.00056 0.0141 0.4496 2780 No

16 19 1 400 0.00056 0.0141 0.4496 3820 No

17 16 2 400 0.001 0.01072 0.2651 2150 No Yes 0

17 16 1 400 0.001 0.01072 0.4573 1890 No Yes 0

17 22 2 400 0.00068 0.0097 0.4566 2100 No

17 22 1 400 0.00069 0.0097 0.4574 2100 No

18 17 2 400 0.00042 0.0018 0.2349 3100 No

18 17 1 400 0.00042 0.0018 0.2349 3460 No

18 23 2 400 0.00138 0.0096 0.4829 1970 No

18 23 1 400 0.00117 0.0096 0.4122 1970 No

20 26 2 400 0.00035 0.0023 0.2249 2780 No

20 26 1 400 0.00035 0.0023 0.2249 2780 No


Appendix D

- 234 -

Line data part 3


TF

phase

shift

- - - kV p.u. p.u. p.u. MVA - - -

20 19 2 400 0.00178 0.0213 0.6682 1590 No

20 19 1 400 0.00132 0.0143 0.3656 1590 No

21 16 2 400 0.00145 0.01824 0.9169 2780 No Yes 0

21 16 1 400 0.00145 0.01824 0.9169 2780 No Yes 0

21 25 2 400 0.00025 0.01 0.1586 2780 No

21 25 1 400 0.00025 0.01 0.1586 2780 No

21 20 2 400 0.0012 0.0048 0.4446 2780 No

21 20 1 400 0.0012 0.0048 0.7 2780 No

21 19 2 400 0.00037 0.0059 0.294 3030 No

21 19 1 400 0.00037 0.0059 0.2955 2780 No

22 16 2 400 0.00178 0.0172 0.8403 2010 No

22 16 1 400 0.00178 0.0172 0.627 2010 No

22 25 2 400 0.00037 0.0041 0.4098 3275 No

22 25 1 400 0.00034 0.0041 0.429 3275 No

22 21 2 400 0.00019 0.00111 0.1232 2780 No

22 21 1 400 0.00048 0.0061 0.3041 2780 No

23 29 1 400 0.00151 0.0182 0.53 2010 No

23 24 2 400 0.00086 0.0008 0.9622 2780 No

23 24 1 400 0.00023 0.0007 2.8447 4400 No

23 22 2 400 0.00055 0.003 0.3468 2780 No

23 22 1 400 0.00039 0.003 0.2466 2770 No

23 29 2 400 0.00151 0.0182 0.53 2010 No

24 28 1 400 0.00068 0.007 0.2388 2210 No

24 25 2 400 0.00104 0.0091 0.2918 1390 No Yes 0

24 25 1 400 0.00104 0.0091 0.2918 1390 No Yes 0

24 28 2 400 0.00068 0.007 0.2388 2210 No

25 26 2 400 0.0002 0.0057 0.532 6960 No

25 26 1 400 0.0002 0.0057 0.532 5540 No

27 26 2 400 0.0002 0.00503 0.1797 3100 No

27 26 1 400 0.0002 0.00503 0.1797 3100 No

28 27 2 400 0.00038 0.00711 0.2998 3070 No

28 27 1 400 0.00038 0.00711 0.2998 3070 No

29 28 2 400 0.00051 0.00796 0.34 2780 No

29 28 1 400 0.00051 0.00796 0.34 2780 No


Appendix D

- 235 -

Reference case solved load flow data

Node V Angle Node

type Pgen Qgen

Shunt

Gain

Shunt

Loss SVCs Q

- p.u. Deg - MW MVAr MVAr MVAr MVAr

1 1.000 48.75 PV 854.00 -49.18 27.00 0.00 0.00

2 1.000 47.27 PV 1264.00 267.04 0.00 0.00 4.50

3 1.000 39.24 PV 780.00 252.63 0.00 0.00 0.00

4 1.000 33.26 PV 2337.00 597.14 0.00 0.00 0.00

5 1.000 29.55 PV 882.00 -28.90 0.00 0.00 0.00

6 1.000 26.20 PV 871.00 244.84 0.00 0.00 0.00

7 1.000 30.68 PV 2047.00 -111.07 9.00 0.00 0.00

8 0.996 30.62 PQ 0.00 0.00 0.00 0.00 0.00

9 1.001 22.24 PQ 0.00 0.00 375.41 0.00 -142.76

10 1.000 21.84 PV 2817.00 233.67 684.00 -120.00 0.00

11 1.000 15.56 PV 4576.00 1189.27 945.00 -220.00 0.00

12 1.000 14.39 PV 3353.00 375.62 328.00 -380.00 0.00

13 0.991 12.18 PQ 0.00 0.00 832.65 -235.93 0.00

14 0.991 15.89 PQ 0.00 0.00 195.60 -432.49 0.00

15 1.000 17.67 PV 6271.80 1243.37 1030.00 -580.00 0.00

16 1.000 16.34 PV 9838.00 3118.90 333.40 -320.00 0.00

17 1.000 8.16 PV 1608.00 356.18 574.86 -60.00 0.00

18 1.000 7.44 PV 1759.00 -45.33 4454.00 -600.00 -99.00

19 1.000 7.38 PV 2614.00 1201.13 412.20 -120.00 0.00

20 1.000 3.33 PV 1254.00 304.42 287.40 0.00 0.00

21 1.000 4.13 PV 535.00 326.00 495.00 -84.00 132.80

22 1.000 3.19 PV 323.00 130.03 2218.00 -300.00 44.00

23 1.000 2.31 PV 6204.84 1254.40 1170.70 -1080.00 113.20

24 0.993 1.45 PQ 0.00 0.00 605.34 -118.31 0.00

25 0.995 -0.95 PV 1708.00 941.00 2376.25 -1901.01 340.40

26 1.000 2.26 PV 4430.00 434.93 352.00 -180.00 0.00

27 1.000 0.00 slack 996.50 416.22 110.00 0.00 0.00

28 1.000 -1.03 PV 1229.00 248.31 1140.00 -440.00 103.70

29 1.000 -1.39 PV 1742.00 -639.90 1452.70 -380.00 -237.80

Appendix D

- 236 -

Diagram of comparative load flow for the GB system [71].

Appendix D

- 237 -

D2. Dynamic Data

Dynamic data for different types of generators

Type H14 H11 N3 F15 CF1 CF2 CF3 CF4

Rated

Power MVA 145 115 500 448 128 192 278.3 375

Rated V kV 14.4 12.5 18 22 13.8 18 20 22

Rated

PF - 0.9 0.85 0.9 0.85 0.85 0.85 0.9 0.9

H - 6.23 7.8 16.5 11.5 5.3 6 8.3 9

D - 2 2 2 2 2 2 2 2

ra p.u. … 0.0024 0.0041 0.0043 0.0024 0.0036 0.0043 0.0045

xl p.u. 0.28 0.147 0.275 0.15 0.095 0.186 0.304 0.14

Xd p.u. 0.953 1.06 1.782 1.67 1.68 1.67 1.675 1.5

Xq p.u. 0.573 0.61 1.739 1.6 1.61 1.64 1.648 1.4

Xd' p.u. 0.312 0.315 0.444 0.265 0.232 0.615 0.311 0.25

Xq' p.u. 0.573 0.61 1.201 0.46 0.32 0.958 0.979 0.44

Xd'' p.u. 0.273 0.25 0.283 0.205 0.171 0.225 0.231 0.18

Xq'' p.u. 0.402 0.287 0.277 0.205 0.171 0.224 0.229 0.181

Tdo' s 7.07 8.68 6.07 3.7 5.89 5 5.4 8

Tqo' s … … 1.5 0.47 0.6 1.5 1.5 0.41

Tdo'' s 0.041 0.04 0.055 0.032 0.034 0.043 0.047 0.036

Tqo'' s 0.071 0.08 0.152 0.06 0.08 0.15 0.15 0.07

Excitation system data

Excitation System DC1A/ST1A Parameters

TR (s) KA TA (s) TE (s) KE VRmax / VRmin

0.01 40 0.02 0.785 1 10/-10

SE=AexeBex

KF TF (s) Tr Ka Ta

Aex=0.07 Bex=0.91 0.1 1 0.01 200 0

Note: A value for KE = 1 is used to represent a separately excited exciter.

Turbine governor data

Hydraulic and Steam Turbine Parameters

Rp Tw (s) TM (s) TG (s)

0.05 2 =2H 0.5

R FHP TRH (s) TCH (s)

0.05 0.333 6 neglected

Appendix D

- 238 -

Allocation of selected generation types

No. Generator

Type

No. of paralleled

Generators

Excitation

Type

1 H14 8 DC1A

2 CF3 6 DC1A

3 H11 9 DC1A

4 F15 7 DC1A

5 N3 2 ST1A

6 WF 20 /

7 N3 5 ST1A

10 CF2 19 DC1A

11 N3 12 ST1A

12 CF3 15 DC1A

15 F15 18 DC1A

16 CF4 33 DC1A

17 F15 5 DC1A

18 F15 5 DC1A

19 CF4 9 DC1A

20 N3 3 ST1A

21 CF3 3 DC1A

22 CF1 4 DC1A

23 F15 18 DC1A

25 CF1 17 DC1A

26 CF3 20 DC1A

27 N3 3 ST1A

28 CF3 6 DC1A

29 N3 4 ST1A

Appendix D

- 239 -

Generation of heavy and light loading conditions

Node

Light loading Heavy loading

Generator

Type

Generation

(MW)

Generator

Type

Generation

(MW)

1 H14 854 H14 854

2 WF 1000 CF3 1264

3 H11 780 H11 780

4 Closed 0 F15 2337

5 WF 2000 N3 882

6 WF 871 WF 871

7 WF 2000 N3 2047

10 CF2 845 CF2 2817

11 N3 4576.00 N3 4576

12 WF 1000 CF3 3353

15 Closed 0 F15 6272

16 CF4 2951 CF4 9838

17 Closed 0 F15 1608

18 Closed 0 F15 1759

19 WF 2000 CF4 2614

20 N3 1254.00 N3 1254

21 CF3 160 CF3 535

22 CF1 97 CF1 323

23 Closed 0 F15 6205

25 CF1 512 CF1 1708

26 WF 1000 CF3 4430

27 N3 665.76 N3 996

28 CF3 387 CF3 1229

29 N3 1742.00 N3 1742

Appendix E

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Appendix E

List of Publications

[C1] L. Shen, M. Barnes, J. V. Milanović, and R. Preece, "Control of VSC HVDC

system integrated with AC network," 10th IET International Conference on AC and

DC Power Transmission (ACDC), December, 2012

[C2] L. Shen, M. Barnes, and J. V. Milanović, "Interactions between STATCOM

and VSC HVDC in dynamic GB system," 7th IET International Conference on

Power Electronics Machines and Drives (PEMD), April, 2014

[C3] L. Shen, W. Wang, and M. Barnes, "The influence of MTDC control on DC

power flow and AC system dynamic responses," IEEE PES General Meeting,

Conference & Exposition, July, 2014

[C4] L. Shen., M. Barnes, J. V. Milanović, K. Bell, and M. Belivanis, “Potential

interactions between VSC HVDC and STATCOM,” 18th Power Systems

Computation Conference (PSCC), Wroclaw, Poland, August, 2014

[C5] L. Shen, W. Wang, and M. Barnes, J. V. Milanović, " Integrated AC/DC

model for power system stability studies," 11th IET International Conference on AC

and DC Power Transmission (ACDC), February, 2015.

[J1] L. Shen, M. Barnes, R. Preece, J. V. Milanović, K. Bell, and M. Belivanis,

“The effect of VSC HVDC control on AC system electromechanical oscillations and

DC system dynamics,” Accepted for publication in IEEE Transactions on Power

Delivery, February, 2015.

model integration and control interaction analysis of ac

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